Of all the ways to knock someone out, a karate chop to the neck is one of the least effective and least reliable ways to do it. Actually, significant impact to the neck and cervical spine is probably more likely to result in serious neurological consequences such as paralysis rather than a simple knockout as shown on tv.

How could a karate chop knock someone out?

There are actually some plausible, if improbable mechanisms:

Vagus Nerve


It's possible that a well-placed strike to the vagus nerve in the neck under the appropriate conditions could render someone temporarily unconscious, however this would not be likely to last more than few seconds. This would be the most likely explanation