A trimming press working apparatus comprising: trimming means for cutting a plate material along a trimming line which divides a product portion from a non-product portion in the plate material; and scrap cutting means for cutting the non-product portion along a scrap severing line intersecting the trimming line, characterized in that, said trimming means includes one trimming press die means having a first cutting blade extending along the trimming line and another trimming press die means for cutting the plate material along the trimming line in cooperation with the first cutting blade of said one trimming press die means, said scrap cutting means includes one scrap cutting press die having a second cutting blade extending along the scrap severing line and another scrap cutting press die having a third cutting blade extending along the scrap severing line so as to cut the non-product portion along the scrap severing line in cooperation with the second cutting blade of said one scrap cutting press die, said trimming line includes a first trimming line portion and a second trimming line portion other than the first trimming line portion, said another trimming press die means includes main trimming press die means having a fourth cutting blade for cutting the plate material along the second trimming line portion in cooperation with the first cutting blade, auxiliary trimming press die means having a movable cutting blade for cutting the plate material along the first trimming line portion in cooperation with the first cutting blade, and liquid pressure generating means for imparting to the movable cutting blade a cutting force based on compressible liquid pressure, said movable cutting blade is movable relative to the fourth cutting blade, said liquid pressure generating means includes a cylinder, a piston disposed in the cylinder, a piston rod having one end coupled to the piston and another end with the movable cutting blade disposed thereon, and a compressible liquid disposed in the cylinder, said compressible liquid is adapted to generate a first liquid pressure to impart the cutting force to the movable cutting blade when the movable cutting blade cuts the plate material along the first trimming line portion in cooperation with the first cutting blade, said liquid pressure generating means is adapted to allow the second and third cutting blades (37, 91) to cut the non-product portion, said fourth cutting blade includes a fifth cutting blade extending along one trimming line portion of the second trimming line portion severed at the first trimming line portion and a sixth cutting blade extending along another trimming line portion of the second trimming line portion severed at the first trimming line portion, said main trimming press die means includes one trimming press upper die integrally having the fifth cutting blade and another trimming press upper die integrally having the sixth cutting blade, said movable cutting blade has a first movable blade surface, and a second movable blade surface intersecting the first movable blade surface, said second cutting blade has a first fixed blade surface opposing the first movable blade surface and a second fixed blade surface intersecting the first fixed blade surface, when, in use, the first movable blade surface of the movable cutting blade of the auxiliary trimming press die means presses the first fixed blade surface of the second cutting blade with the non-product portion of the plate material located therebetween, a large raising force is applied to the movable cutting blade owing to its reaction force, and when, in use, this large raising force is applied to the piston through the piston rod, the compressible liquid is compressed to allow the relative raising of the movable cutting blade with respect to the one and other trimming press upper dies (55, 56), and the another scrap cutting press die. trimming means for cutting a plate material along a trimming line which divides a product portion from a non-product portion in the plate material; and scrap cutting means for cutting the non-product portion along a scrap severing line intersecting the trimming line,