Variations will be found with the lower band's spring behind or in front of the band, and this system was borrowed for some of the early US military rifles as well. The lower band uses the same system but instead of having a peg there is a ledge that rests against the edge of the band and which prevents its movement. The spring has a lump on the side toward it's front that is meant for thumb pressure to push the spring down into the stock and the front peg out of the hole in the band. Some Mausers use a later version of this system that uses a much slimmer spring with a long round tail that is inserted in a hole in the stock, a much thinner spring with a round peg on the end that fits into a corresponding hole in the front band. Once you have the front band depressed you can tap it forward with a small plastic or rubber mallet toward the muzzle by tapping against the bayonet lug, and for the lower band by tapping forward against the sling swivel lump. If yours is reluctant to depress you can try tapping it downward with an appropriately sized wooden dowel which won't mar the finish, or a small clamp with an appropriate pad can also be used.

Sometimes it is difficult to depress the band as many haven't been removed since the rifle was manufactured and can have accumulated rust or crud under the band, but originally they were able to be depressed with just firm thumb pressure. So to remove the band you need to force the spring down at the band end into the stock out of connection with the band, and while keeping it depressed you need to tap the band forward toward the muzzle.

These are actually sort of a spring that has a tail on the end farthest away from the band that is fitted into a hole in the stock which is invisible when the spring is in place, and a hook or projection that snaps under the band when it is in place.

If you look at the bottom of the stock you may see what appear to be flat metal bars inletted into the wood and extending backward from the bands. I do not have an 1895 in my accumulation, but Mauser bands are usually held onto the stock in one of two similar ways.

Spanish mauser disassembly