始末
しまつ · shimatsu · JLPT N1 · noun
disposal
始 (beginning) + 末 (end): from the very start to the very end, you handle the whole thing
始末 joins 始 'beginning' and 末 'end', so it covers the whole course of a matter from start to finish. Its sense of disposal comes from tidying up that full course, including the closing work.
末 — tree 木 with extended top stroke marking the tip
末 is an indicative character: it shows the tree 木 with an emphasized horizontal line near the top to point at the treetop, the 'tip' or 'end' of the branches. From this concrete sense it extended to mean 'end,' 'final,' or 'minor/trivial' (as opposed to the root 本).