A saw will make quick work of cutting up firewood or wood for pioneering.
Note: folding saws are designed to be pulled. Pushing a tempered saw blade can cause it to bend or snap
Bow Saws are designed to cut while pushing and have more support than folding saws.
Pull Saw with Folding Saw
Saw with Bow Saw
Open and Close a Folding Saw without drawing blood
Assembling and Disassembling a Bow Saw
Pull Saws are designed to be - you probably have already guessed - to be pulled. Pushing a pull saw forcefully to saw can brake the blade and doesn't work very well because of the way the teeth are sharpened.
Cable Saws are much easier to use if you make a handle for them. Consider constructing a Sapling Bowsaw or a Bucksaw.