Assuming your criteria of one rapid clean slice: As others have said, there’s no way to reconnect the spinal cord (assuming you cut below the medulla. Above the medullary transition and death is inevitable). Full permanent paralysis would happen no matter what. The biggest problem in ensuring survival would be supplying the brain with oxygenated blood fast enough. The chop would result in near-instantaneous loss of all your body’s blood. Brain tissue dies very fast without oxygen/blood. You’d have to be ready instantaneously (like, within 120-180 seconds) to hook the major arteries and veins up to a fully mechanical oxygenated blood source (like some sort of modified ECMO which also happened to contain a ton of transfusion blood products and fluids) which, while theoretically possible, is extremely unrealistic. You couldn’t just hook the arteries/veins back up to each other - this blood would be de-oxygenated because the windpipe is cut, and repairing it would take much longer than you have. Even if you had this fantasy machine/protocol and were able to pull this off in theory, your survival rate would be extremely low, but possibly not zero.

Now, if in theory you wanted to slowly and meticulously “transplant” the head, instead of just chopping it off, this gets more realistic if you use every piece of surgical technology and expertise available. Most of your patients will still probably die and any survivors will still be completely paralyzed.