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You should not need to remove anything once you have taken the lug nuts off. The Mazda symbol can be removed by s thin flat head screw driver or a knife. There should be a big axle nut under the cap, but you should not need to remove it.
The Mazda symbol in the middle just pops right out.
You need to take off all the lug nuts, and then the whole rim should come off. You may want to tap it with your hand around the edges and it should just come off. The whole rim comes off you will not be able to get the tire off by itself.
Mechanic
Does it look like the axle nut is also holding the rim?