puzzle vs mix up

puzzle is a noun but mix up is not a noun.

Word	Noun	Adjective	Verb	Adverb
puzzle	Yes	No	Yes	No
mix up	No	No	Yes	No

As verbs, mix up is a hyponym of puzzle; that is, mix up is a word with a more specific, narrower meaning than puzzle:

Other hyponyms of puzzle include stump, riddle, elude, escape.

puzzle (noun)	mix up (noun)
a game that tests your ingenuity
a particularly baffling problem that is said to have a correct solution

puzzle (verb)	mix up (verb)
be a mystery or bewildering to	cause to be perplexed or confounded
be uncertain about; think about without fully understanding or being able to decide	assemble without order or sense