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
Wiktionary has your exact example
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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.