Mind takes a nominal as its object.
[1] Would you mind stopping walking?

=> there are two objects here,
stopping and
walking.
[2] Would you mind stop walking?

=>
mind takes an -
ing word.
Stop doesn't have -ing.
[3] Would you mind stopping?
Other examples,
- Would you mind if I asked you to stop walking?
- Yes, I would mind if you asked me to stop walking.
Adele, hope that helps in some way.