How do I cut down a bathroom wall drain?
You'd need to reduce the entrance (easy, fittings are made) and RAISE the pipe in the wall (possible but a relatively huge amount of work/expense.) So I'm not quite sure what you mean with "cut down" the drain pipe.

As shown in the pictures, I'm inclined to say cut a notch in the back of the drawer for pipe clearance, and get the reducer you need to go from the drain you have to the tailpiece (the Ikea plumbing you have.)

Alternatively, cut as much as you need off the base of the vanity unit, but if you've already mounted it, that will be a pain, and if you like the height of the countertop now, it would change.

Responding to comment - if it's glued ABS pipe (as I would appear to be) you'd cut it off at the back of the fitting that's on there and glue on an elbow - there appears to be enough pipe behind the fitting to do that. If threaded, you'd unscrew the fitting and screw on an elbow. Reduced or not reduced it will run into the drawer if going straight out. I'm unclear where you are going to fit plumbing and traps with two drawers evidently in the space they'll need, unless there's some sort of room off to one side.

Additional note: - you really should fill in around those water pipes. That type of convenient opening into the back of cabinets is loved by The Uninvited Guests That Travel and/or Live In The Walls.