Method for the press-hardening of a sheet steel material, wherein a moulding process and a cutting operation are performed in one press stroke, comprising the following steps: - providing a tool (100, 100a) which is installed in a deformation press, said tool having at least two tool parts (200, 300) which are movable relative to one another in a working direction and between which a heated sheet steel material can be moulded by application of a pressing force acting in a working direction, and having at least one cutting device by way of which a cutting operation can be performed on the sheet steel material situated between the tool parts (200, 300), characterized in that the cutting device has at least one cutting slide which is movable transversely with respect to the working direction and by way of which, after the moulding of the sheet steel material, a cutting operation can be performed in a section extending at a steep angle relative to the working direction, wherein at least one of the tool parts (200, 300) is formed with at least one cooling device (230, 330) for the active cooling of a tool active surface (222, 322), but the cut line for the cutting operation that can be performed by the movable cutting slide runs in a steeply angled section which is not actively cooled; - placing a heated sheet steel material into the opened tool (100, 100a), wherein the sheet steel material, before being placed into the tool (100, 100a), has been heated to a temperature of over 900°C; - closing the tool (100, 100a) and moulding the sheet steel material, wherein the sheet steel material bears against the tool active surfaces (222, 322) and, in this way, rapid cooling of the sheet steel material is effected which leads to hardening of the sheet steel material; and - subsequently performing at least one cutting operation with the cutting device, in at least one section extending at a steep angle relative to the working direction, for the purposes of trimming and generating a defined outer contour, wherein the cut line profile lies outside actively cooled tool active surfaces (222, 322) and is situated in sections in which, during the prior deformation, the sheet steel material has been cooled less or has not been cooled and therefore, in said sections, has not hardened or has hardened only very slightly, and wherein the sheet steel material is cut while in a still-heated state between 600°C and 700°C. - providing a tool (100, 100a) which is installed in a deformation press, said tool having at least two tool parts (200, 300) which are movable relative to one another in a working direction and between which a heated sheet steel material can be moulded by application of a pressing force acting in a working direction, and having at least one cutting device by way of which a cutting operation can be performed on the sheet steel material situated between the tool parts (200, 300), characterized in that the cutting device has at least one cutting slide which is movable transversely with respect to the working direction and by way of which, after the moulding of the sheet steel material, a cutting operation can be performed in a section extending at a steep angle relative to the working direction, wherein at least one of the tool parts (200, 300) is formed with at least one cooling device (230, 330) for the active cooling of a tool active surface (222, 322), but the cut line for the cutting operation that can be performed by the movable cutting slide runs in a steeply angled section which is not actively cooled; - placing a heated sheet steel material into the opened tool (100, 100a), wherein the sheet steel material, before being placed into the tool (100, 100a), has been heated to a temperature of over 900°C; - closing the tool (100, 100a) and moulding the sheet steel material, wherein the sheet steel material bears against the tool active surfaces (222, 322) and, in this way, rapid cooling of the sheet steel material is effected which leads to hardening of the sheet steel material; and - subsequently performing at least one cutting operation with the cutting device, in at least one section extending at a steep angle relative to the working direction, for the purposes of trimming and generating a defined outer contour, wherein the cut line profile lies outside actively cooled tool active surfaces (222, 322) and is situated in sections in which, during the prior deformation, the sheet steel material has been cooled less or has not been cooled and therefore, in said sections, has not hardened or has hardened only very slightly, and wherein the sheet steel material is cut while in a still-heated state between 600°C and 700°C.