I can tell you for a fact that you will break a few of the clips that hold the the plastic to the door. You can buy replacements at your Mazda dealer. However, I find that you don't actually need all the clips to have to replace the panel. I 'purposely' leave a few out of the clips just for the purpose I can take the panels out whenever I need to.
The rear doors is more difficult to take out than the front because the top of the panel is connected to the window sill.
First, take out the screws from under the tiny rubber mat (inner handle?) and then pop out the plastic cover in the door lever and remove the screw there too.
Then start on the inner bottom (towards the hinge) and yank strongly in a controlled force, but don't go incredible Hulk or your will break 'all' the clips. BTW, even if the clips are broken in half, it still can be used.
So, if you are removing the left rear door panel, you would start at position south-east and yank, then south and yank, south-west and then yank, west and yank, north-west and yank, then north-east and yank.
Finally, the north section has two clips, where you 'feel' you will break it but it won't. You need to yank that off too. DO NOT TUG. YANK!
Once you have the panel out, take out the lever and disconnect the power window cable from the panel. You press down on the release and it should be able to be take out.
That should remove the panel for you. Not hard, but I figured it out with no manual, nobody to show me nor no youtube clips, so anybody can do it.