I've removed my swing arm a few times now on a couple of Monts and the nut is definately on the right hand side (kickstart) as shown in the diagram. With the nut removed it is simply a case of using a copper drift/ nylon faced hammer to get the bolt/axle moving, once moving you need a long drift to drive the bolt out. Once everything is out and cleaned I use Silkolene Pro RG2 synthetic grease which seems to resist water quite well, apply generously and remove excess when assembled.
This has been the case on the 2 Monts that I've had from new, if someone has had the bike before you then the swing arm bolt may have been refitted from the wrong side which would lead to your confusion.
Hope this helps