When Keaton sees his wife's boss coming to pick her up in the limo he runs to get a chainsaw. When you next see him and hear the chainsaw going if you look at the chain on the chainsaw it is not moving. The teeth of the saw are not moving so he could not have been cutting anything.
Chainsaws possess what is known as a "clutch." This allows the engine to run without the chain moving, making the saw much less dangerous. When the clutch is engaged, the chain moves and one may cut wood.
http://www.ankn.uaf.edu/VS/chainsaw.html describes a chainsaw clutch very nicely.
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