Axes made of all types of materials were used with a certainty. Bronze, iron, steel and even stone axes when none of the better materials (ie. metals) were available. I'd argue that well motivated and capable men could fell quite a large diameter trees without too much effort.
From wikipedia I gathered that axes were invented in mesolithic period and saws around neolithic. That's about ca. 6000 bc for axes and around 3000 bc for saws, so they have both been around for a quite bit.
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