I have a surface 3 and the battery has swollen causing g the screen to bulge if I remove the battery will it work from power supply cable without battery I installed
I think you can.
I have seen many laptops be used without a battery and they work fine. I have even seen them without screens as well! But as @spikey_richie said, you will probably deform the laptop, and create problems for the laptop in the future. It is not a good idea to leave a laptop designed with a battery to have no battery. It was designed to have it in there.