My rear tire went flat and it was dry rotted as well.  Thought i would replace.  I have new tire and tube in but i went to pull the old one off and i ran into trouble.  I cant get the axle shaft out.  It spins easy enough.  I lifted tire and moved at lots of angles.  hit with rubber mallet.  I figured the axle shaft would just slide right out, but NO, lol.   Not even close to easy.  is there a trick i'm missing?  i dont want to mess the threads up.  There is a cir clip that appears to hold bearing in on the threaded side of axle shaft.    do i need to pull it?   Thanks in advance cause i am land locked with flat tire.

Take a small 1/4" punch and a hammer and smack the center of the threaded side of the axle 3 three times and shout ( I WANNA GO HOME ).

Poof the axle is on the ground in Kansas... forevermore 

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Here is what im fighting.  I will take a punch and wish im back in Kansas.  Just did not want to screw something up.

Level the shaft to the hub and use a bigger hammer. Clean up the shaft with some steel wool, probably corroded is all.

No question that at this point you will want new seals and bearings, as this will probably ding them. But that will be a nice addition to the brakes shoes and tire, tube, and rim strip, right?

The rotation was the bearings working as they should; the freeze of the axle is just old age. BTW, how are your knees these days?

Once its off the bike... You may as well rejuvenate it... Makes most effective use of this process..
Sneezles61

 You probably got it out already but here are a few more...
  There is a steel spacer on the right side that can rust onto the axle bolt. Holding it still while turning the bolt & applying heat etc can break it free.
  Laying the bike on its right side with a piece of wood supporting swing arm gives a more solid support and better angle for you as your hitting.  
 Leave the nut on loosely as your hitting the end that way you can test turn it now and then to be sure the threads are not being mushroomed out

Here's my method that never fails on swinging arm rusted in bolts. Same with the rear axle. Steel tube with a good foot onto the concrete & in your case you'll need someone to hold a solid steel rod of similar size to your axle. I'd weld a long handle so you're helper can get out of the way, then a good hit & it'll be on the way. 

Thanks to all. Got it out for sure. used a brass punch and a hammer instead of rubber mallet. It appears all is good. for sure i need to evaluate all parts mentioned.

Congratulations!