"Cut off" clearly implies separation, which is exactly what is meant by "punishment" in the context of God's eternal punishment of the unrepentant sinner.
No, the parallel isn't of life and death (annihilation) in Matthew 25:46, but of the gift of eternal life for the righteous and the eternal punishment of the unrepentant wicked. This is what the verse explicitly contrasts, not your "logical antithesis."
Catholic eschatology so focused on eternal punishment in Hades, the OT basically became irrelevant. But Christ and His apostles only had the OT. "Cutting off" is what happened to transgressors:
KJV Gen. 17:14 And the uncircumcised man child whose flesh of his foreskin is not circumcised, that soul shall be cut off from his people; he hath broken my covenant.
KJV Exod. 12:15 Seven days shall ye eat unleavened bread; even the first day ye shall put away leaven out of your houses: for whosoever eateth leavened bread from the first day until the seventh day, that soul shall be cut off from Israel.
KJV Exod. 12:19 Seven days shall there be no leaven found in your houses: for whosoever eateth that which is leavened, even that soul shall be cut off from the congregation of Israel, whether he be a stranger, or born in the land.
KJV Exod. 31:14 Ye shall keep the sabbath therefore; for it is holy unto you: every one that defileth it shall surely be put to death: for whosoever doeth any work therein, that soul shall be cut off from among his people.
KJV Lev. 7:20 But the soul that eateth of the flesh of the sacrifice of peace offerings, that pertain unto the LORD, having his uncleanness upon him, even that soul shall be cut off from his people.
KJV Lev. 7:21 Moreover the soul that shall touch any unclean thing, as the uncleanness of man, or any unclean beast, or any abominable unclean thing, and eat of the flesh of the sacrifice of peace offerings, which pertain unto the LORD, even that soul shall be cut off from his people.
KJV Lev. 7:25 For whosoever eateth the fat of the beast, of which men offer an offering made by fire unto the LORD, even the soul that eateth it shall be cut off from his people.
KJV Lev. 7:27 Whatsoever soul it be that eateth any manner of blood, even that soul shall be cut off from his people.
KJV Lev. 17:10 And whatsoever man there be of the house of Israel, or of the strangers that sojourn among you, that eateth any manner of blood; I will even set my face against that soul that eateth blood, and will cut him off from among his people.
KJV Lev. 19:8 Therefore every one that eateth it shall bear his iniquity, because he hath profaned the hallowed thing of the LORD: and that soul shall be cut off from among his people.
KJV Lev. 20:6 And the soul that turneth after such as have familiar spirits, and after wizards, to go a whoring after them, I will even set my face against that soul, and will cut him off from among his people.
KJV Lev. 22:3 Say unto them, Whosoever he be of all your seed among your generations, that goeth unto the holy things, which the children of Israel hallow unto the LORD, having his uncleanness upon him, that soul shall be cut off from my presence: I am the LORD.
KJV Lev. 23:29 For whatsoever soul it be that shall not be afflicted in that same day, he shall be cut off from among his people.
KJV Num. 9:13 But the man that is clean, and is not in a journey, and forbeareth to keep the passover, even the same soul shall be cut off from among his people: because he brought not the offering of the LORD in his appointed season, that man shall bear his sin.
KJV Num. 15:30 But the soul that doeth ought presumptuously, whether he be born in the land, or a stranger, the same reproacheth the LORD; and that soul shall be cut off from among his people.
KJV Num. 15:31 Because he hath despised the word of the LORD, and hath broken his commandment, that soul shall utterly be cut off; his iniquity shall be upon him.
KJV Num. 19:13 Whosoever toucheth the dead body of any man that is dead, and purifieth not himself, defileth the tabernacle of the LORD; and that soul shall be cut off from Israel: because the water of separation was not sprinkled upon him, he shall be unclean; his uncleanness is yet upon him.
KJV Num. 19:20 But the man that shall be unclean, and shall not purify himself, that soul shall be cut off from among the congregation, because he hath defiled the sanctuary of the LORD: the water of separation hath not been sprinkled upon him; he is unclean.
To be "cut off" from the people of God is to be denied access to the "tree of life", which results in eternal death. Hence the usage in Mt. 25:46, its idiomatic. Destruction or eternal death from which there is no resurrection, is the result of being "cut off."
Punishment for the obstinate soul was "cutting off" that resulted in death. We see that belief in a Aramaic Targum of Num. 15:31:
“He shall be cut off in this world, and that man shall be cut off in the world to come, and bear his sin in the day of judgment.-Owen, J. (1854). An Exposition of the Epistle to the Hebrews (W. H. Goold, Ed.; Vol. 18, p. 503). Johnstone and Hunter.
This does not deny eternal punishment for those who deserve it. But not everyone deserves it. For example,
the THREAT OF ETERNAL TORMENT for taking the Mark of the Beast would have no meaning if all sinners receive eternal torment.
Therefore, less than eternal torment for less sin must exist or the THREAT has no meaning:
9 And the third angel followed them, saying with a loud voice, If any man worship the beast and his image, and receive his mark in his forehead, or in his hand,
10 The same shall drink of the wine of the wrath of God, which is poured out without mixture into the cup of his indignation; and he shall be tormented with fire and brimstone in the presence of the holy angels, and in the presence of the Lamb:
11 And the smoke of their torment ascendeth up for ever and ever: and they have no rest day nor night, who worship the beast and his image, and whosoever receiveth the mark of his name. (Rev. 14:9-11 KJV)