"ant," late 14c. (early 14c. as a surname), from pyss "urine" (said to be in reference to the acrid smell of an anthill) + mire "an ant," probably from Old Norse maurr "ant" (cognates: Swedish myra, Danish myre, Middle Dutch miere, Dutch mier, Crimean Gothic miera "ant"), from PIE base *morwi- (see Formica (2)). Compare pissant, also early Dutch mierseycke (from seycke "urine"), Finnish kusiainen (from kusi "urine").
He is as angry as a pissemyre, Though þat he haue al that he kan desire. [Chaucer]
