Doing such stunts is punishable.
The example above has a clause as a Subject. We can parse it like this:
- [Doing such stunts] is punishable.
When the Subject of a sentence is a clause, we always see singular verb agreement:
- That she is not here yet is problematic.
- For her to do that is undesirable.
It does not matter if the clause has an expressed Subject or not:
- Eating babies is wrong
- To forgive is noble.
If we use plural verb forms when we have a clause as a Subject, the result will be ungrammatical:
- *That she is not here yet are problematic. (ungrammatical)
- *For her to do that are undesirable. (ungrammatical)
- *Eating babies are wrong. (ungrammatical)
- *To forgive are noble. (ungrammatical)
For this reason we need singular verb agreement in the Original Poster's sentence. Why? Because:
- *[Using plural verb forms with clausal Subjects] are ungrammatical. (ungrammatical)