We observe helical dislocation network in twisted bilayer graphene (tBLG), which is accompanied by large out-of-plane deformation. By atomistic calculations, we demonstrate two distinct out-of-plane deformation modes, breathing mode with small out-of-plane deformation and bending mode with one order larger corrugation magnitude compared to the breathing mode. The out-of-plane deformation is caused by inhomogeneous interlayer coupling resulting from the periodic stacking order of the tBLG moiré superlattice. Instead of commonly observed screw dislocation in tBLG, we demonstrate a slip-induced helical dislocation network in the bending mode tBLG. We show that bending mode deformation is more stable at low twist angles, as the energy savings due to interface energy exceeds the energy penalty due to the strain energy caused by the large out-of-plane deformation. Our work provides a detailed picture of a new helical dislocation structure in tBLG and establishes a direct connection between the dislocation and deformation. Therefore, understanding the dislocation mechanics of tBLG may open up the possibility to control the corrugation, and reveal an opportunity to tune the intriguing physical properties of twisted bilayer graphene.