Can you get a absessed tooth removed without antibiotics?

Possibly. You can have it extracted if you are able to open your mouth wide enough to allow for the dentist to have access to the area. Many practitioners may not feel comfortable doing the extraction with an infection however, extracting the tooth will clear the infection quickly and the dentist could then place you on antibiotics after extraction to totally clear the infected area.
Yes. If you are able to tolerate the treatment well enough and the infection is still low, antibiotics are sometimes not needed. The size of the infection may dictate that you need to take antibiotics, however. Please discuss the risks and benefits in great detail with your dentist.