Japanese kokuji (国字). From 占める (shimeru), as cursive form of top component ト (also 〆). Then applied to other kanji of the same pronunciation, namely 締め, 閉め, 絞め, and 搾め, all pronounced しめ shime. Sense of “closed, fastened” is due to 閉める (shimeru, “to close”) and 締める (shimeru, “to fasten”).
〆 is primarily used as an abbreviation for 締め, most commonly in 〆切, as an abbreviation for 締切 (shimekiri, “deadline; locked (door)”), also 締める (〆る) and 締高 (〆高). It is also sometimes used for 閉め, notably in sense of “closed envelope”. Even more rarely, it is used to abbreviate other kanji, including 絞め, 占め, and 搾め, as in 〆粕, (from 搾め糟 (しめかす)). There is also occasional use of 乄, as in 乄高.