For removing axles without a slide hammer, I've had success using a length of chain bolted to a lug stud and the other end wrapped and bolted to a sledge hammer. It's no where near as convenient, but can generate a lot of impact force to pull the axle. Of course you have to careful not to get clobbered by the axle when it comes flying out.
If the bearings are retained in the axle housing after the axle is removed, a slide hammer is probably going to be needed unless you have some type of puller that will work. If you don't own a slide hammer, many of the auto parts stores rent tools like this for free or low cost, with just a deposit until the tool is returned.