It is believed that the name of Cuttyhunk derives from the Wampanoag word "Poocutohhunkunnoh," which probably means “point of departure” or “land’s end,” a fitting title as it is the outermost island in the Elizabeth island chain off the coast of Massachusetts.

Sources:

http://en.wikipedia.org/wiki/Cuttyhunk

http://www.cuttyhunk.net/History.shtml

Also as a brief aside: Do you have an interest in MA or the South Shore, since this seems like a pretty niche question? (I only ask because I'm a long time MA resident who has spent some time on the island lol)