why harborfrieght grinder get hot while cutting?

A die grinder? Those are Garbage. Get a used DeWalt.

I Tried to fix Two of these, in a few minutes, brushes worn completely thru. Shorts in the armature. Plenty of "grease in the gears". i checked this, first

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"fixing it"? Cost much more to rewind it than its worth. Might be poorly designed and burn up, again. It isn't the 'fifties. Much cheaper to get a used De Walt  than even bother with the HF.

Harbor Freight tools are often not very good. Their electric power tools tend to be underpowered and easily overloaded to the point of burning up. You get what you pay for. If you just need something for a one time job they will usually get you through it though.

You use too much, no resting. 

Harbor Freight Chinese stuff is imitation quality of heavy duty commercial equipment!

It may have been assembled with too little grease in the gearbox.  Usually just a few screws holds that part together, wipe out as much old grease as you can and pack it full of a good quality synthetic, don't force the tool when using it, and allow it to cool occasionally.  Those types of motors are not meant for continuous duty.

That is normal.  The grinder cuts due to friction on the blade  Friction causes heat.

Pushing it too hard

Due to friction and force exerted 

It is cheaply made.

Because you were using it to cut instead of grind!

Do you mean the cutting disc or the body of the tool? The disc gets hot because of the  large friction of the cutting process. Any electrical tool with a motor gets a bit warm with heavy use, that is normal. If it is 'screaming hot' then possibly there is an internal problem, which would need diagnosing and fixing by a competent person.