A cutter (4, 6) for hot-cutting a rod, preferably a rod of steel, comprising: - a frame; - a cutting element, which is fitted to said frame, comprises an arc-shaped cutting surface extending about a first axis, is adapted, in use, to cut said rod, and defines an open seat bound by said cutting surface; and - releasable connecting means for releasably connecting said cutting element and said frame; said connecting means being also releasably connected to said frame; said cutting element comprising a radially external surface and said frame being bound by a first and a second wall (20, 21) which are opposite to each other and lie on respective planes orthogonal to said first axis; characterized in that said cutting element is axially clamped between said connecting means and said frame along said first axis; said connecting means comprising at least one bracket; said second wall axially bounding said frame on the side of said cutting element; said radially external surface being axially clamped between said second wall and said at least one bracket along said first axis; said cutter (4, 6) further comprising a pair of guides (55,) which extend spaced apart from one another; said guides being releasably fitted to respective sides of said second wall; each said guide comprising a relative main surface, which is orthogonal to said first axis and is adapted to slide over a corresponding further surface of a further guide of a further cutter (6, 4), so as to avoid the interference between cutting surfaces of said cutter (4, 6) and said further cutter (6, 4); said cutting element extending symmetrically about said first axis and comprising: - a disk, which extends about a further axis parallel to said first axis A; - a pair of head surfaces, which protrude from an axial end of said disk along said first axis, are spaced from one another along said second axis; said second axis being orthogonal to said first axis and - said cutting surface, which extends between said head surfaces and protrudes from said disk towards said first wall; said disk comprising, proceeding radially to said first axis and on the opposite radial direction to said first axis: - a ring orthogonal to said first axis and defining an axial end of said cutting surface; - an edge inclined with respect to said first axis; - an additional surface orthogonal to said first axis; and - said radially external surface orthogonal to said first axis. - a frame; - a cutting element, which is fitted to said frame, comprises an arc-shaped cutting surface extending about a first axis, is adapted, in use, to cut said rod, and defines an open seat bound by said cutting surface; and - releasable connecting means for releasably connecting said cutting element and said frame; said connecting means being also releasably connected to said frame; - a disk, which extends about a further axis parallel to said first axis A; - a pair of head surfaces, which protrude from an axial end of said disk along said first axis, are spaced from one another along said second axis; said second axis being orthogonal to said first axis and - said cutting surface, which extends between said head surfaces and protrudes from said disk towards said first wall; - a ring orthogonal to said first axis and defining an axial end of said cutting surface; - an edge inclined with respect to said first axis; - an additional surface orthogonal to said first axis; and - said radially external surface orthogonal to said first axis.