From Proto-Vietic *p-sət ~ *p-sat. Cognate with Muong Bi thắt, Chut pəsat⁷. Also compare Mang hat⁷ (“to turn off”) (from earlier *s- through regular debuccalization in Mang), Kuy pəsat ("to extinguish").
Unlikely to be related to Proto-Bahnaric *pat (“to extinguish”), Proto-Katuic *pat (“extinguished (of fire)”), Proto-Khmuic *-pət (“to extinguish”), unless there was an infix *-s- (which is otherwise unknown within Austroasiatic) or metathesis of a presyllable (*s-p- > *p-s-). The first scenario can almost be safely disregarded, but the second is slightly more plausible since this root is attested both on its own and accompanied by presyllables and/or prefixes across Austroasiatic branches, plus the existence of the Souei cognate above. Still, it might just be coincidental.
(This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium.)