For one thing, avsluta can never be used with the infinitive. You can say sluta prata! ('stop talking!'), but you can't use avsluta that way. I'm not sure we never use sluta with nouns, but at least I can say we usually don't. So I'd say Jag måste avsluta samtalet 'I must finish the conversation', but I wouldn't use sluta that way.
No, I meant that you can't use it together with another verb in the infinitive. You can use it with a noun, but not with a verb.
Avsluta samtalet! 'Finish the conversation!' = imperative + noun
With Sluta you can use it with a verb: Sluta prata! 'Stop talking!' – but you can't do that with avsluta.