a heap, and Mow, to cut down, are quite different words. Mow, a heap, is the Anglo-Saxon mowe, but mow, to cut down, is the Anglo-Saxon máw-an.
There is a third Mow (a wry face), which is the French moue, as “Faire la moue à [quel qu'un],” to make faces at someone, and “Faire la moue,” to pout or sulk. (Dutch, mowe.)
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894