To achieve a useful raising of the ISS orbit, you would need to have a tether that could temporarily carry a strain representing an appreciable fraction of the ISS's total mass.

You also have to do it twice. Once to make the orbit elliptical with a higher apogee (but the same original perigee) and once to raise the perigee, so you need TWO shuttles, or Progress supply ships.

To avoid damage to the ISS or the Shuttle by the recoiling tether when it is cut, you either need to cut both ends with close synchroneity, or have some sort of run-out mechanism or a sideways ejection rocket for the tether stump. (or a really complicated catcher mechanism to save you using a new length of strong (massive) tether cable each time.

It gets complicated, making it work for big, expensive, man-carrying things...