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I can’t for the life of me get this tire off this riding mower. Please help, it’s a Craftsman

First off I don’t see any rust removal of the axle, you need to get it shiny clean. Second, I have found that a lot of penetrating oil sprayed on the front and back of the shaft helps. Problem is probably rust buildup in the keyway is most often the problem. Keep working the rim in and out, cleaning the shaft each time and adding oil will slowly get it off.

I use a pair of scissor jacks between the rim & the mower in combination with an air hammer
The process is to put some weight on the rim with the jacks, not too much , fingers only
Then I put a allan bolt in the hole in the axel
With a point chisel, blunted off so it sits tight in the head of the allen bolt, lean into the axel and pull the trigger
As the wheel starts to come off the jacks will slip
So then it is tighten the jacks again & repeat

A word of warning

The axel is only held in with a small clip. either a C clip or a wire gear retainer so can be ripped out if you do the jacks up Chuck Norris tight
All you are doing is taking up the slack in the axel so the blows from the hammer have nothing to resist them and th axel should be able to move in by the same distance you moved the wheel out .

It is not a 5 minute job but done this way there will be no damage to wheel, axel or diff .
As per Rivets above , plenty of penetrating oil ( WD 40 is not a penetrating oil )
Tapping the key with a pin punch usually helps because the keyway is where most of the rust starts

Now you know why wheels should come off every 4 to 4 years and get greased

For those i don't meas around. I go straight to the oxy/propane torch and the garden hose then finish the job with a can of spray paint.

For re-assembly I'd suggest wiping key & key-way & axle shaft, etc with a high temp grease.. Just thin layer to prevent this dealio again..

From Photo #2 it appears that the key is not IN the Keyway, binding the Wheel, Try to put the key back in its' place.
Perhaps the key has sheared off or the wheel has become loose on the shaft or both. Spray into the keyway from both sides with penetrant and let sit for a couple days
Use Larger Bolts on the Puller and rattle the end with an Air Chisel attachment when it it tight. If you pull the axle out of the tranny the entire machine is Junk. If you are just changing a tire, get that side up in the air and Remove the Tire. Not hard.
Clean rim and install tube if tire is salvageable. When mounting, use a Vise~Grips on the bead edge to keep tire from sliding around. Lube tire bead first.

If the rim will move any at all on the axle get some 2 fuel mix and pour some on the axle area. This will soak in and help loosen the rust.

Why do you need the rim off? I have changed tires while still on the mower. Not easy, but possible.
You don't want to pull the axle out of the transaxle, it would turn into a different thread.

reported spamer

There are two guys out there, multiple posts, reported both of them.

you get the rope and the horse, I'll find the tree. I absolutely will not spend 1 cent to someone who spams me. That includes political parties too.

You need to line up the key with the keyway slot spray a good rust buster on the axle and key then try pulling with the puller but i would use bigger bolts