The sense of the expression is most clear when the expression is read in context:
Woe unto them! for they have gone in the way of Cain, and ran greedily after the error of Balaam for reward, and perished in the gainsaying of Core. These are spots in your feasts of charity, when they feast with you, feeding themselves without fear: clouds they are without water, carried about of winds; trees whose fruit withereth, without fruit, twice dead, plucked up by the roots; raging waves of the sea, foaming out their own shame; wandering stars, to whom is reserved the blackness of darkness for ever.There is a natural structure to this passage:
The first is set of three parallels:
- have gone in the way of Cain, and
- ran greedily after the error of Balaam for reward, and
- perished in the gainsaying of Core"
Next, there is a bridging passage: "These are spots in your feasts of charity, when they feast with you, feeding themselves without fear"
The point here is obvious: these men ought to be afraid to feast with believers, and they are a blemish on such feasts. Whether Jude means the Lord's Supper here, or whether he simply means other meals [fn2] does not appear to be central. The point is that these men shamelessly mix in with believers, and this a bad thing.
Finally, there are a series of descriptions of the men:
- clouds they are without water, carried about of winds;
- trees whose fruit withereth, without fruit, twice dead, plucked up by the roots;
- raging waves of the sea, foaming out their own shame;
- wandering stars, to whom is reserved the blackness of darkness for ever
The second description itself has a series of items:
- whose fruit withereth,
- without fruit,
- twice dead,
- plucked up by the roots"
The third description is of a tree [fn4] that is completely dead [fn5]. Those familiar with certain varieties of trees will recognize that if one cuts down a living tree, leaving only a stump, new life can spring from the stump. A tree cut down is not always a tree that has been completely killed. But a tree that is twice dead would be one whose root lacks any reserves, such that it could sprout again. It is completely and thoroughly dead.
The final description takes it a step further. A tree that is plucked up by the roots is absolutely hopeless. No matter how dead a stump may look, and even if there are no sprouts yet, one might hope that while the root is in the ground there is some hope. There is no hope for these, their root is out of the soil - they have been uprooted.
The point of the series of descriptions is the result of the progression. There is no hope for these on whom Jude is pronouncing woe. The blackness of darkness - one of several images of hell - is reserved for them forever, just as the elect have heavenly mansions awaiting them.
 Yes, I mean "Jude 12" not "Jude 1:12." One should try to avoid using the chapter number for books that have only one chapter. It is easy to forget this rule - I'm sure a careful study of my blog would find me making that error myself.
 The Geneva Bible's notes state: The feasts of charity were certain banquets, which the brethren who were members of the Church kept altogether, as Tertullian sets them forth in his apology, chap. 39.
 To my shame, it was only in assembling these footnotes, that remembered to check what Manton had already stated this:
We go on with the verse. Trees whose fruit withereth, twice dead, plucked up by the roots. This is the second similitude; here are four properties of evil trees reckoned up by way of gradation.and again:
Obs. 1. Now, in this description you may observe a gradation:—(1.) ‘Whose fruit withereth;’ (2.) ‘Without fruit;’ (3.) ‘Twice dead.’ First bad fruit, and then leaves, and then rottenness. Note, that deceivers and hypocrites ‘grow worse and worse.’ You have it from the apostle Paul also, 2 Tim. iii. 13, ‘But evil men and seducers shall wax worse and worse, deceiving and being deceived.’ They deceive others, and the devil deceiveth them. The two states are not at a stay; wicked men grow worse and worse, and godly men grow better and better. Observe, then, which way is your progress and growth. The glory of the Lord, in Ezekiel, departed by degrees: first from the holy place, then from the altar of burnt-offering, then the threshold of the house, then the city, then the mountain which is on the east side of the city; it stood hovering there, as loath to be gone. So the Spirit of God doth not all at once depart from men, but by degrees. First men suspect duties, then dispute against them, then shake them off, and then come to beastliness and profaneness. Or, if you will, take the gradation thus:—First, God is cast out of the closet, private intercourses are neglected; then out of the family; then out of the congregation, and public ordinances seem useless things; and then blasphemies and a profane vertiginous spirit ensueth. First, men begin to wrangle, and sceptically to debate matters of religion, and within a while to oppose the truth: ‘The beginning is foolishness, and the latter end is mischievous madness,’ Eccles. x. 13. To this sense of taking the expression as a whole to be about the tree agrees Calvin (whose agreement, I must confess, I discovered only after the fact):
Peter adds the similitude of a dry and empty fountain; but Jude employs other metaphors for the same end, that they were trees fading, as the vigor of trees in autumn disappears. He then calls them trees unfruitful, rooted up, and twice dead; as though he had said, that there was no sap within, though leaves might appear.Likewise Manton agrees, as can be seen at footnote  above.
 To this sense of "twice dead" agree:
Twice dead; wholly dead; dead over and over; dead by nature, and dead by that hardness of heart they have contracted, or that reprobate sense to which God hath given them up.and
Twice dead; that is, entirely, thoroughly, and really dead in trespasses and sins, notwithstanding their pretensions to religion and godliness; or the sense may be, that they were not only liable to a corporeal death, common to them with all mankind, but also to an eternal one, or to the death both of soul and body in hell. Homer calls (d) those διθανεις, "twice dead", that go to hell alive: or rather the sense is this, that they were dead in sin by nature, as all men are, and again having made a profession of religion, were now become dead to that profession; and so were twice dead, once as they were born, and a second time as they had apostatized:and
(d) Odyss. l. 12. lin. 22.
The next evil property, taken from trees and applied to men, is δὶς ἀποθανόντα, twice dead. If you apply this to the trees, they may be twice dead, either in regard of fruit, as a barren thing is said to be dead, as ‘the deadness of Sarah’s womb.’ Rom. iv. 19; or, in regard of substance, rotten and like doaty trees, growing worse and worse; or ‘twice dead,’ by a Hebraism, ‘very dead,’ as double is put for much. But now, if you look to the reddition of this similitude, these seducers are ‘twice dead,’ both in regard of their natural estate, ‘dead in trespasses and sins,’ and their apostasy, or decay of that life which they seemed to have by the grace of the gospel, wilful defection making their case incurable, Heb. vi. 5, 6, 2 Peter ii. 20.And again:
Obs. 2. Again, I observe, men that fall off from the profession of the truth are twice dead. To natural they bring on judicial hardness; when they seemed to make some escape from the misery of nature they relapse into it again, and then their chains are doubled; as a prisoner that hath once broken prison, if taken again, is laden with irons. Two ways do natural men come to be twice dead—by custom in sinning, and by a revolt from God after they had given their names to him. By custom in sinning, for by that means they are hardened in their way, and ‘given up to a reprobate mind,’ so as to lose all sense of sin, Rom. i. 26-28; and by revolt from God; those that will, after trial, forsake him, no wonder if God leave them to their own choice, to be held under the power of the devil, by a dark and foolish heart.(I commend Manton's entire discussion, which may be found here.)
Matthew Henry writes:
The text speaks of such as were twice dead. One would think to be once dead were enough; we none of us, till grace renew us to a higher degree than ordinary, love to think of dying once, though this is appointed for us all. What then is the meaning of this being twice dead? They had been once dead in their natural, fallen, lapsed state; but they seemed to recover, and, as a man in a swoon, to be brought to life again, when they took upon them the profession of the Christian religion. But now they are dead again by the evident proofs they have given of their hypocrisy: whatever they seemed, they had nothing truly vital in them.and
Clement of Alexandria:
"Woe unto them!" he says, "for they have gone in the way of Cain." For so also we lie under Adam's sin through similarity of sin. "Clouds," he says, "without water; who do not possess in themselves the divine and fruitful word." Wherefore, he says, "men of this kind are carried about both by winds and violent blasts." "Trees," he says, "of autumn, without fruit,"— unbelievers, that is, who bear no fruit of fidelity. "Twice dead," he says: once, namely, when they sinned by transgressing, and a second time when delivered up to punishment, according to the predestined judgments of God; inasmuch as it is to be reckoned death, even when each one does not immediately deserve the inheritance.