If your language has homonyms/homophones, words with double meaning, or even combinations of words that kind of phonemically produce another word when put together, it can have puns. It doesn't matter if you find them funny or not. The only way there can be no puns in Slovak is if it's a robot language where there's absolutely no room for homophony or double entendre whatsoever, or a nigger language that only has so many words and little morphology or syntax to speak of. Probably the latter.