This kanji is said to depict an elephant (its ancient form) being put to work by a human hand, emphasizing its use for **doing** tasks **for** people. Think of an elephant performing a useful **act**.
'Tame' — You must **tame** an elephant **for** it to be useful and **do** tasks. This directly links the reading 'tame' (ため) to the meanings 'for' and 'do'.