I think the name "whip" came from the rapid long arm motion possible with a two man saw.

Or possibly from the "whupp" noise that such a saw makes, at the point where the direction changes. This is caused by a flexing of the blade as the tension changes from a forward to a backward motion. (Forward/backward are used relatively, in this case - there is no front or back to a whip saw!)
You can tell the expertise of the sawing team, to some extent, by how little "whupp" they make.