This is not an objective, anatomical term, neither does it imply coitus. It connects with that extension of meaning of the unprintable, a fool, or a person whom one does not like. ["Dictionary of Rhyming Slang," 1960]Thorkelin, in the essay on the Berserkir, appended to his edition of the Krisini Saga, tells that an old name of the Berserk frenzy was hamremmi, i.e., strength acquired from another strange body, because it was anciently believed that the persons who were liable to this frenzy were mysteriously endowed, during its accesses, with a strange body of unearthly strength. If, however, the Berserk was called on by his own name, he lost his mysterious form, and his ordinary strength alone remained. ["Notes and Queries," Dec. 28, 1850]The adjectival use probably is from such phrases as berserk frenzy, or as a title (Arngrim the Berserk).
Our Gayness and our Gilt are all besmyrcht. ["Henry V," IV.iii.110]
Related: Besmirched; besmirching.The connection of the senses is very loose; some of them appear to have arisen quite independently of each other from different applications of BE- pref. [OED]