The present disclosure relates to a cutter clamp (8, 37) that comprises a first arm part (10, 39) and a second arm part (11, 40), where the arm parts (10, 11; 39, 40) are arcuate and arranged to adjustably at least partially enclose a major part of a circumference (57, 63) having a center (58, 64). The cutter clamp (8, 37) comprises at least one hollow rod (21, 22; 48, 62) arranged for receiving a mounting rod (36) for a power cutter (1, 56) in a pivoting manner. The smaller circumference the arm parts (10, 11; 39, 40) are adjusted for, the closer to the center (58, 64) said hollow rod (21, 22; 48, 62) is moved. The present disclosure also relates to a cutter clamp attachment device (68), a cutter clamp kit and a cutter clamp holding frame (76).