Offhand, I can recall that Baron Sunday in "Never On A Sunday" was able to mentally torture Clark (with physical results). I think it's up to the author to make a case for it in their story, but I know I personally would believe there's more than one way to hurt him. As long as you can explain why I would imagine you could torture him any way you please.

Lois: You know, I have a funny feeling that you didn't tell me your biggest secret.

Clark: Well, just to put your little mind at ease, Lois, you're right.
Ides of Metropolis