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]