1620s, earlier raspis berry (1540s), possibly from raspise "a sweet rose-colored wine" (mid-15c.), from Anglo-Latin vinum raspeys, origin uncertain, as is the connection between this and Old French raspe, Medieval Latin raspecia, raspeium, also meaning "raspberry." One suggestion is via Old Walloon raspoie "thicket," of Germanic origin. Klein suggests it is via the French word, from a Germanic source akin to English rasp (v.), with an original sense of "rough berry," based on appearance.
A native plant of Europe and Asiatic Russia, the name was applied to a similar vine in North America. Meaning "rude sound" (1890) is shortening of raspberry tart, rhyming slang for fart.