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1640s, "to disable, render useless," a figurative verbal extension from the noun hamstring "tendon at the back of the knee" (1560s), from ham "bend of the knee" (see ham (n.1)) + string. Cutting this would render a person or animal lame. Related: Hamstrung.
[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]
hamstring ham·string (hām'strĭng')
Any of the tendons at the rear hollow of the human knee.
hamstrings The hamstring muscle.
The large tendon in the back of the hind tarsal joint of the quadruped.