1530s, from spear (n.2) + mint (n.1). "Said to be a corruption of spire-mint, with reference to the pyramidal inflorescence" [Century Dictionary].
Entries linking to spearmint
spear n.2
"sprout of a plant," 1640s, earlier "church spire" (c. 1500); variant of spire (n.).
mint n.1
aromatic herb, plant of the genus Mentha, Old English minte (8c.), from West Germanic *minta (source also of Old Saxon minta, Middle Dutch mente, Old High German minza, German Minze), a borrowing from Latin menta, mentha "mint," itself from Greek minthē, personified as a nymph transformed into an herb by Proserpine, which is probably a loan-word from a lost Mediterranean language. For mint-julep, see julep.