Correction: In standard Greek mythology (Hesiod's Theogony, Apollodorus), Medusa and her two sisters—Stheno and Euryale—were all immortal Gorgons.
The common belief that Medusa alone was mortal stems from Ovid's Metamorphoses (8 CE), where Perseus beheads her—implying mortality. But earlier and parallel traditions describe all three as immortal monsters.
Why the confusion? Ovid's version became dominant in Roman and post-Renaissance art/literature. In it, Medusa was once a beautiful priestess raped by Poseidon in Athena's temple; Athena cursed her with snakes and petrifying gaze—making her mortal and killable. Her sisters remained immortal.
Scholarly consensus: Archaic Greek sources (Hesiod, 700 BCE) depict all three as immortal, chthonic monsters. The mortal Medusa is a later literary innovation.