sluta is the infinitive and slutar is the present tense. In English, it's harder to see the difference because the infinitive is usually the same as the present – for everyone except 'he' and 'she'.
If you look at these sentences:
He wants to quit - here '(to) quit' is an infinitive
He quits and I quit – here 'quit' and 'quits' are in the present tense.
So if you stick to the third person, it's easier to see the difference in English. After do/does, you have the infinitive, which is why you don't say "He does not stops" here. But in Swedish, we don't use the 'do' construction, instead we just have the present tense, Han slutar = 'He stops'