SQL Only allows you to SELECT data in Marketing Cloud, so removing data from a field is not something a SELECT will allow you to do. You can always delete single-record data from a data extension using Contact Builder, but if you're looking to do it en masse with SQL there's a hacky way to do it:
Create an empty duplicate of your data extension where you copy over all your desired data, less the timestamp data in question. Then just copy it all back to the starting data extension.
Edit: You mention the data extension has this field as not nullable. You can't have null data in a field that's not nullable. You'd need to change the rule or duplicate the data into a different data extension where it is nullable.