If your clips aren't holding down your build plate, make sure your nozzle isn't crashing into the plate and moving it. A build surface between the clip and surface or adhesive might help keep the clip from slipping on the top surface. A rubbery gasket material that can withstand you heated bed temperatures, such as the silicon FarO mentions, ...
I'm not sure what "the build plate keeps slipping while printing. I tried to use binder clips to keep the plate in place" means, but if you have a build surface and a bottom heated bed, you can look for "silicone thermal pad 0.5mm".
You can put it between build surface and lower bed, so that it will increase friction and there won't be ...
I use kapton tape to fixate the glass plates to the heated beds on two of my printers, one a Prusa i3 clone, the other a CoreXY. The tape is able to withstand higher temperatures, and is very thin, so it doesn't have the drawbacks of limiting the print area or high chance the nozzle hitting the clips.
Once a time, it was the same with me, I sanded the surface well and continued for a while without any problems. The only problem was the sand pattern that was always visible in the bottom of models and finally I upgraded the bed to PEI sheet.
If you have tried every trick to remove the print, you probably need to replace the build surface. If the PLA is "engraved" into the build surface, your surface is damaged anyways, just replace the surface, or remove the top surface and buy a sheet of glass, preferably borosilicate.