A tissue-removing catheter for removing tissue from a body lumen includes a tissue-removing. The tissue-removing element may be coupled to a first longitudinal body portion of the catheter body. The first longitudinal body portion may be rotatable along its length and relative to a second longitudinal body portion to adjust the angular position of the first longitudinal body portion relative to the second longitudinal body portion. An angular-positioning mechanism may be operatively connected to the tissue-removing element for rotating the tissue-removing element relative to the second longitudinal body portion about a rotational axis to adjust an angular tissue-removing position of the tissue-removing element, relative to the longitudinal axis of the body lumen, from an first angular tissue-removing position to a second angular tissue-removing position offset from the first angular tissue-removing position.