execution on a feudal lord's command
Historical term referring to an execution carried out under the direct order of a feudal lord, typically in the context of samurai justice.
上意討ち is a historical term for an execution carried out on the orders of one's feudal lord.
打ち首 is beheading as a form of execution, not necessarily tied to a feudal lord's direct order, whereas 上意討ち emphasizes the authority behind the execution.
Compound of 上意 (じょうい, 'lord's will') and 討ち (うち, 'strike/kill'), literally 'striking down by the lord's will'. The exact historical derivation is uncertain, but the term is associated with feudal-era samurai practices.