A back-up roll device and method for conducting corner deformation on a chamfered continuous casting slab. The back-up roll device includes back-up rolls with α-angle bevels, movable bearing seats, bearing seat moving rails, bearing seat motion holding mechanisms and inner arc or outer arc frames of a casting machine. The back-up rolls are arranged on the inner and/or outer arc frames of the horizontal segment of the casting machine. Support surfaces of the back-up rolls make contact with and squeeze smaller obtuse angles adjacent to the wide face of the inner or outer arc on the chamfered continuous casting slab, and therefore each smaller obtuse angle is squeezed into two larger obtuse angles. The back-up roll device and method for conducting corner deformation on the chamfered casting slab can achieve the purposes of eliminating edge slivers.