Please correct me if I'm wrong, but I think that "to know" and only some other verbs have a completely different negative verb. Like 알다 becomes 모르다 (to not know), but for most other verbs you can just say 안 + the conjugated verb or add -지 않다. Adding -지 말다 actually means "don't (do) x" as a command rather than "I don't do (x) ". So 하지 마 means don't do (it), and 가지 마 means don't go, etc. Vs 하지 않아 which means I don't do (it). You can use 안 and 지 않다 interchangeably to mean "I don't do x", but 안 + verb is more casual/common. :) And in cases where there is a different verb for the negative, I think you use that instead.
"Does not know" is "몰라요" with ㅗ whereas "ask" is "무러요" (i forgot if there is one or two ㄹ) with ㅗ and "cry" is "우러요" (again, don't know if there is one or two ㄹ), which doesn't have a ㅁ and is with ㅜ. (Hope it helps and sorry for the eventual mistakes, English isn't my first language ^^')