Generally speaking, it is safe to cut Polaroid pictures. You will not risk harm to yourself or the immediate environment around you. But, cutting into a Polaroid picture will expose the internal components to air, and that exposure can significantly shorten the overall lifespan of the Polaroid picture.
The key to a good Polaroid of a phone or computer screen is to control the lighting. Soft lighting is very important, and you want to consider a lower shutter speed to get better image quality. Alternatively, you can use a Polaroid printer or third-party service to directly print a Polaroid of a digital image.