Which is the correct sentence in the examples below?
He didn't mentioned anything?
or He doesn't mentioned anything?
He didn't told me?
or He didn't tell me? (Since, I believe we should not use two past tenses in the same sentence)
When using did as an "auxiliary" or "helper" verb to form the past tense, it is used with the bare infinitive of the verb in question, the "lexical" verb.
He didn't mention anything.
He didn't tell me.
Here we form the past tense using the lexical verb only, which is a shade more formal:
He mentioned nothing.
He told me nothing about that.
To form the past tense of some verbs, we add the -ed ending to the bare infinitive (mention -> mentioned). With other verbs, the vowel changes (tell -> told).