Yes, it's acceptable when do replaces a verb already stated: Do you speak French? Yes, I do.
It also works in comparisons: She sings better than I do.
It fails when there's no earlier verb to replace: I more than he does leaves the final do with nothing to stand in for, so name the action instead, as in I travel more than he does.
When you're answering a question
When someone asks a question your sentence answers, end it with do. Reply to Do you speak French? with Yes, I do. The final do stands in for speak French, so the answer sounds natural.
Does she live nearby? is answered No, she doesn't., and that final doesn't is the sentence's last word. Ending with doesn't is acceptable here because it stands in for live nearby after the auxiliary has already appeared. The auxiliary-do article covers how to pick the short-answer form; this bullet is about the ending position itself, and doesn't closes the sentence the same way plain do does.
When you're comparing yourself to someone, let do close the clause. Say She reads more than I do. The final do replaces read, and the sentence is complete as it stands.
When no verb has been stated earlier, do can't close the sentence. I more than he does doesn't work on its own; name the action first, like I travel more than he does.
When it won't work on its own
Yes, you can end a sentence with do, but only when it stands in for a verb already stated. In She works late and I do too, the final do replaces works late, so the sentence feels complete as it stands.
In comparisons, the final do has to stand in for the same verb on both sides. He enjoys chess more than I do works because do stands in for enjoys chess, so each side compares the identical idea. If the sides use different verbs, the comparison collapses: I do more than he enjoys chess leaves the final do pointing at nothing, because the verb being compared on his side is enjoys, not do. Reword it so one verb covers both sides, like He enjoys chess more than I do.
It fails when there's no earlier verb for do to replace. Yes, I do on its own answers nothing if nobody asked or claimed anything, so name the action instead, like Yes, I speak French.