The invention relates to a coil (2) of cutting wire for a vegetation cutting machine, wherein the wire (20) is coiled on itself about an axis so as to form at least two temporarily bonded turns (21) and a central void (22), characterized in that the surface of the wire portion forming the innermost turn of the coil facing the central void (22) comprises a plurality of grooves (230) creating a succession of protrusions and recesses extending parallel to said axis.The invention also relates to a cutting assembly for a vegetation cutting machine such as a border trimmer or a brush cutter, said assembly including at least one coil (2) according to one of claims 1 to 9 and a cutting head (1) comprising:a body (10) defining an inner recess for the coil (2) and provided with a peripheral opening (12a, 12b) for the emergence of a length of cutting wire separated from the coil, and capable of being driven in rotation by a motor, anda central mandrel (13) for supporting said at least one coil, said mandrel comprising at least one arrangement (135″) adapted to cooperate with the grooves (230) of the coil so as to ensure rotational engagement between the mandrel and the coil, the mandrel being able to selectively rotate relative to the body.
