Lr CC stores your original photos in the cloud. Your hard drive may be filled up for other reasons. Check the preference settings mentioned by selondon first. These will help minimize the amount of data being downloaded to your computer from Lightroom CC.
After you import your photos to LrCC on your surface pro, you can remove them from the computer. I recommend moving them to an external hard drive for safe keeping, before deleting them from the computer. Are your original photos still on the surface pro, after you imported them into Lightroom?