Depending upon which of the 9,854 different MTD mowers you are talking about either the bolt is a coach bolt so you will need to rotate it till the square engages then push down on the head while you turn the nut or slip a thin spannar onto the head.
Second method cut a slot in the end on the bolt with a cut off wheel deep enough the cut the nut in 1/2 and replace both the bolt & the pulley
Or as above but use a Dremmel or similar and hold the bolt with a screwdriver.
Use a nut splitter.
If it is a front engined ride on, pull the battery out, cover the fuel cap or drain the tank to prevent spills, then stand the thing on it's bum so you have clean access to the underside.