finish sth.的意思是:结束某事;完成某事。如:
Haven't you finished your homework ? 难道你还没有完成家庭作业吗?(《牛津高阶英汉双解词典》第9版p.807)
finish with sth.的意思是:用完某物;不再使用某物;不再做某事。如:
When you've finished with the book, can I see it ? 这本书你看完以后我能看吗?(《牛津高阶英汉双解词典》第9版p.808)
I've finished with gambling. 我已戒赌了。(同上)