STOP and QUIT need object like "stop smoking". The object is in type of verb+ ~ing, gerund in English. In Korean, the verbs 그만두다, 중단하다 for stop or quit need object in form of verb+기(Korean gerund -> a noun).
ie) I stopped reading a book. 나는 책읽기를 그만두었다. (reading 책읽기 / 읽다 -> 읽기)
I quit drinking 나는 술마시기를 그만 두었다 -> 나는 술을 끊었다(마시다 -> 마시기 - - -> noun 술)
You use "stop + ~ing", but Korean use mostly "stop + a noun(or sometimes gerund)". So you'd better translate "stop + ~ing" into "stop + a noun".
ie) I stopped smoking. 나는 담배를 끊었다.
I quit trying 나는 노력을 멈추었다[그만 두었다]
I quit going to school 나는 학교를 그만 두었다