Old English piþa "pith of plants," also "essential part," from West Germanic *pithan- (source also of Middle Dutch pitte, Dutch pit, East Frisian pit), a Low German root of uncertain origin. Figurative sense was in Old English. Pith helmet (1889, earlier pith hat, 1884) so called because it is made from the dried pith of the Bengal spongewood.
"to kill by piercing the spinal cord," 1805, from pith (n.). Related: Pithed; pithing.