I just removed the power steering pump and A/C from my car, bracket , hoses and all.The A/C has been disconnected for some time.The power steering blew out on the way home today.I had been meaning to remove the compressor for some time , it was easier with the power steering unit out of the way, and one thing led to another.....
Anyway , when I first disconnected the belt for the power steering and test drove it (checking for the leak) there was no beep.I took out the pump and compressor , removed the bracket , and only unplugged the harnesses to the pump and the one ground wire to the A/C compressor.Plugged the holes left in the rack and put the battery back.
As soon as I cranked the car the CPU started this non-stop beeping.There are no idiot lights on, all the guages are reading fine , and the car runs great.I did have to readjust the idle to compensate for the missing pump.Any ideas on why its beeping now? Is there something in the harness I need to jump out?

 

By 'cpu' you presumably mean the power steering control unit (as opposed to the 'cpu' that controls hazards, brake lights, horn, lighting delay etc).
Anyway there's 6 different buzzer tones it'll produce depending on the error condition.
A constant tone indicates a control unit malfunction. One to five short beeps then a delay indicates what error the control unit perceives as existing. In 3 of those 5 cases it indicates a problem with power steering inputs, like broken or shorted wires, so a removed ps unit would certainly qualify !
A bit more info is needed...

 

the beep tones and such sorry i didnt help you more but if you have a mazda manual then take a look or grab your buddies

 

This may help. This may not help. One day I went to drive the car. The beep, beep , beep almost drove me nuts. Finaly found out that the three position interior light assy above your head caused my probleml. I switched it to the center or right, whatever and the beep stopped. I never thought it out as to why. Just relieved to not hear that sound.

 

Some cars have speed sensitive power steering, computeized, including yours apparently. Under the dash, under the instrument cluster area, there is a box for the power steering. Unplug it. This should fix your beeping.

 

as said above your power sterring is controled by it's on computer under the dash. that's where the beeping is comming from. unplug it.