We were coming down a fast, narrow stream in early spring. On a bend in the stream was a full-width strainer; an obstruction spanning from shore to shore. After a short debate, we opted to cut it rather than unload and carry around it. So we poled a boat out into the current and held it stationary with a pole and chopped the log, which was slightly underwater, with an axe. The canoe is on the upstream side of the log; the current is moving from left to right.
You won’t find this in any books on axe use, but the problems you’re tasked with solving on an expedition rarely fit nicely into the training scenarios you practice. In order to solve them it usually takes a lot of skill and a lot of creativity.