A top sub, for connection to a tubing string of a production well, has a first engagement structure, and a mandrel has a second engagement structure. A coupling engages the first and second engagement structures. A housing covers an internal space of the tubing swivel, in which the coupling is located. The coupling includes a first coupling structure having a shape complementary to a shape of the first engagement structure and a second coupling structure having a shape complementary to a shape of the second engagement structure. One of (i) the first engagement structure and the first coupling structure and (ii) the second engagement structure and the second coupling structure has a clutch mechanism to enable the top sub to be rotated in a first direction relative to the mandrel and to rotate the mandrel with rotation of the top sub in a second direction opposite the first direction.