A method for removing a portion of a crystalline material (e.g., SiC) substrate includes joining a surface of the substrate to a rigid carrier (e.g., >800 μm thick), with a subsurface laser damage region provided within the substrate at a depth relative to the surface. Adhesive material having a glass transition temperature above 25° C. may bond the substrate to the carrier. The crystalline material is fractured along the subsurface laser damage region to produce a bonded assembly including the carrier and a portion of the crystalline material. Fracturing of the crystalline material may be promoted by (i) application of a mechanical force proximate to at least one carrier edge to impart a bending moment in the carrier; (ii) cooling the carrier when the carrier has a greater coefficient of thermal expansion than the crystalline material; and/or (iii) applying ultrasonic energy to the crystalline material.