That's what several standard Bible translations would have you think. The verse in question is 1 Corinthians 6:13a, and it turns out that a decision of punctuation makes all the difference in two contrasting understandings of Paul's attitude toward the human body. Let me illustrate by showing you four different translations of this one verse. Pay close attention to the quotation marks included (not by me but) by the translation team.
"Food is meant for the stomach and the stomach for food"-- and God will destroy both one and the other (ESV).
You say, "Food was made for the stomach, and the stomach for food." (This is true, though someday God will do away with both of them) (NLT).
"Food is meant for the stomach and the stomach for food," and God will destroy both one and the other. (NRS)
You say, "Food for the stomach and the stomach for food, and God will destroy them both." (TNIV).
Did you catch that? Each of these translations agree that Paul is quoting a slogan original to the Corinthians, but they disagree on the extent of the quotation. The first three close the quote before the assertion that God will destroy both stomach and body; the fourth closes the quote after that claim. To their credit, the translators of the NRSV include a footnote saying that "the quotation may extend to the word other." But the question remains. Whose view are we faced with? Should the claim that God will destroy the body be attributed to Paul or to a group of Corinthians?
The problem arises because the Greek in which Paul wrote did not have quotation marks; so the translators have to decide where to close the quote when rendering it into English. To make this decision they must consider the verse in its immediate context and in light of all Paul's letters. In this case, the decision about punctuation is really a decision about interpretation and how we understand Paul's anthropology. What does Paul believe to be the destiny of the human body? Punctuation matters.
In this case, I would argue that the TNIV gets it right. The next verse tells us Paul's view of the future of the believer's body, "God raised the Lord and will also raise us by his power" (NRSV). For Paul, the future resurrection of the body is an argument against the libertine attitude of appetite indulgence among some of the Corinthians. The body (and its parts) will be resurrected in a manner analogous to that of Jesus. That means that physical (though certainly transformed) bodies will arise from their graves. The corpse of someone who is in Christ will not be destroyed; it will not even remain a corpse. To the contrary, it will be made alive again by the power of God. It seems to me unclear how we can describe that as destruction.
Paul has more to say about death and resurrection in chapter 15 of the same letter, where the language of destruction comes up again, but not with regard to the body. Paul says that, at the coming of Christ, death is the thing that will be destroyed when the bodies of believers are raised from the dead (15:26). Death is the enemy of Christ, and Christ will destroy his enemies. The final enemy that Christ will destroy is death itself. We might say that, as the nails spring loose from the coffins of those who belong to Christ, the final nail will be hammered into death's own coffin.
Paul fills in the picture later in the same chapter by saying that the presently mortal and perishing body will be overcome with immortality and imperishability (see especially vv. 50-55). The body will be transformed, not destroyed. I see no way that this transformation could plausibly be construed as destruction; it is the opposite of destruction.
This evidence weighs strongly against an interpretation (or punctuation!) of 6:13a that attributes to Paul the belief that God will destroy our bodies. Destruction is defeat. Resurrection is victory. Destruction is what happens to death. Resurrection is what happened to the body of Christ, and it's what will happen to the bodies of those who belong to Christ.