How would you translate The Martian's: "I'm going to science the s*** out of this"? This is China's in theater subtitle version: 我得他妈的想办法活下去

A streaming video version: 只能开动脑筋想办法自救

Can you do better than the above? Namely by incorporating science into it, both of which don't include the science bit.

Why didn't the translations use 科学 as a verb? It seems many words serve as 
a noun or a verb.

Something like this -只能开动脑筋用科学想办法自救 ?
科学 could indeed function as a static verb, but it is not recognized as a regular verb. Neither was 和谐, until it became a fad using it to criticize mainland politics (as in 他被和谐了). As in English, you could formally make most nouns verbs, but it only works if people understand the logic behind the transformation.

As for 科学, you could probably use the 化 suffix to accomplish what you want: 要科学化这个该死的问题想个办法。