I couldn't come up with a short title, but the upside is that there is not much needed to be said in the body of the question!
For @dmr (and others), it mixes “let's cross that bridge when we come to it” and “burn one's bridges”.
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Seems these are called malaphors
An informal term for a blend of two aphorisms, idioms, or clichés (such as "That's the way the cookie bounces").
A blend of malaproprism and metaphor, coined by Lawrence Harrison in the Washington Post article "Searching for Malaphors" (Aug. 6, 1976)
Wiktionary has your exact example
Examples include "hitting the nail on the thumb", "barking up the wrong alley" and "We'll burn that bridge when we come to it".
I believe the term for this is mixed metaphor
This is where you take two common metaphors and mix them together, often incorrectly, to make a metaphor that doesn't make sense.
For example, mixing "You can't have your cake and eat it" with "It's not over till the fat lady sings" might produce "It's not over till you've had your fat lady and eaten it".
If your particular example is meant as a joke, then I would say that it is a pun.