Pulling clamp for continuous rod or coiled tubing strings

A pulling clamp is provided for releaseable connection to a blunt, uphole string end of a continuous string. A main clamp body has clamp bore therethrough and having a string-receiving opening at the pulling end for receiving the string end, an actuating bore at the pulled end and a tapered bore therebetween. A taper insert having a radially compressible gripping bore is beatable in the tapered bore and axially actuable between a passive first receiving position, for receiving the string end, and the active second gripping position for radially compressing the taper insert about the string end for actively gripping the string end therein. The taper insert can be axially actuated using a threaded main body and threaded top cap for sandwiching the taper insert therebetween, the top cap being threaded axially into and out of the pulled end of the main body between the passive and active positions.