Arduino and Ramps powering up

I want to run 2 stepper motor using Arduino mega 2560 and ramps 1.4 and somehow i got by Arduino burned while connecting motor when i plug the board to computer.my question is- Can i plug external power supply and USB connection to computer at the same time WHEN THE STEPPER MOTOR IS CONNECTED TO ARDUINO MEGA? please help.
CAN WE ATTACH OUR ARDUINO MEGA WITH RAMPS 1.4 TO USB WITH COMPUTER WHILE IT IS ALREADY POWERED UP WITH EXTERNAL SUPPLY WHEN THE STEPPER MOTOR IS CONNECTED?

It depends on the supply and on the computer. Usually it is not a problem but as you have found, this kind of thing can happen.

If your computer is a laptop then you can unplug it from the wall and work on battery while connected to the Arduino. That will stop any strange power supply issues.