Page 35 of the Instruction Manual shows how to remove the base plate from a 13-round mag. Step 1 says to just slide the baseplate off of the bottom of the magazine while holding the floor plate catch down!
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Well, that's not easily done! There is a hell of a lot of spring pressure pushing on that plate and I can never get it started to slide off with just my fingers.
I have had to resort to sticking the blade of a small flat-blade screwdriver into the seam where the baseplate separates (on both sides of the floor plate catch) and twist the blade a bit to get the baseplate to start sliding off. (The seam between the baseplate and the bottom of the mag shown in figure 72, the arrow pointing at the control spring. That seam when the baseplate is still in it's fully installed position is where to put the screwdriver blade.)
Use a small thin-blade screwdriver and be gentle with your twisting motion. You're prying on plastic. Once you get the base plate just barely started to slide off with the screwdriver you will be able to pull it the rest of the way off with your fingers. And, don't forget to keep your thumb holding the floor plate catch down. Once the baseplate comes off the spring is gonna shoot out of there hard if you're not holding it.
PS) 10-round mags are different. They have a button to push on the bottom to get the baseplate off.
*BTW, you really should have the Instruction Manual for your firearm. If you don't have one for your M&P, go on S&Ws web site and click on "Support" then "Owner's Manuals" to download one.