A cutter 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 (A), 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 which are opposite to each other and lie on respective planes orthogonal to said first axis (A); characterized in that said cutting element is axially clamped between said connecting means and said frame along said first axis (A); 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 (A); said cutter 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 (A) and is adapted to slide over a corresponding further surface of a further guide of a further cutter , so as to avoid the interference between cutting surfaces of said cutter and said further cutter ; said cutting element extending symmetrically about said first axis (A) 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 (A), are spaced from one another along said second axis (X); said second axis (X) being orthogonal to said first axis (A) 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 (A) and on the opposite radial direction to said first axis (A): - a ring orthogonal to said first axis (A) and defining an axial end of said cutting surface ; - an edge inclined with respect to said first axis (A); - an additional surface orthogonal to said first axis (A); and - said radially external surface orthogonal to said first axis (A). - a frame ; - a cutting element , which is fitted to said frame , comprises an arc-shaped cutting surface extending about a first axis (A), 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 (A), are spaced from one another along said second axis (X); said second axis (X) being orthogonal to said first axis (A) 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 (A) and defining an axial end of said cutting surface ; - an edge inclined with respect to said first axis (A); - an additional surface orthogonal to said first axis (A); and - said radially external surface orthogonal to said first axis (A). <EOS>