c. 1600, from German Hamster, from Middle High German hamastra "hamster," probably from Old Church Slavonic chomestoru "hamster" (the animal is native to southeastern Europe), which is perhaps a blend of Russian chomiak "hamster," and Lithuanian staras "ground squirrel." The older English name for it was German rat.
1640s, "to disable, render useless," a figurative verbal extension from hamstring (n.) "tendon at the back of the knee." Cutting this would render a person or animal lame. Literal sense of the verb is attested from 1670s. Since it is a verb from a noun-noun compound, hamstrung as a past participle is technically incorrect.
[I]n hamstring, -string is not the verb string; we do not string the ham, but do something to the tendon called the hamstring; the verb, that is, is made not from the two words ham & string, but from the noun hamstring. It must therefore make hamstringed. [Fowler]