The overall answer is that YES, Spinal Manipulative Therapy (SMT) is safe, but with some caveats.
This study was a meta-analysis of studies of the risk of cervical spinal manipulation. They chose the best 118 studies. The most frequently described adverse events were stroke, headache, and vertebral artery tear. Fifty-four reviews (46%) expressed that is safe, 15 (13%) expressed that SMT is harmful, and 49 reviews (42%) were neutral or unclear.
Thirteen reviews reported incidence estimates for serious injuries, roughly ranging from 1 in 20,000 to 1 in 250,000,000 manipulations. In general, the reviews that were of the highest quality found that the risk was low. They noted that, although it is hard to draw definitive conclusions, the types of injuries reported can be significant. Thus, there is some risk with spinal manipulation.
My take on this is that more gentle spinal mobilization, which has been found to have almost NO RISK, drops the chance of serious injury closer to zero. Note: This study did not differentiate "mobilization" from "manipulation." However, in general, the studies they chose were using high velocity cervical manipulation. The Syst Rev. 2017 Mar 24;6(1):64.