gramatická analýza: ... děl básník mna si nos
The main conjugated verb is děl. The subject for the verb is therefore masc. sg. básník. Mna is a present verbal adverb, masculine sg form of mnout. The verbal adverb adds information to the main verb, what the person was making an utterance.
Try paraphrasing the sentence another independent clause: "the poet said and at the same time (současně or přitom) rubbed his nose."