A method is provided for separating a portion from a sheet-like glass or glass ceramic element along an intended separation line to divide the element into the portion and a main part. The method includes producing filamentary damages a volume of the glass or glass ceramic element adjacently aligned along the separation line, the filamentary damages are produced by laser pulses of a laser, the glass or glass ceramic element comprises a material that is transparent for the laser pulses; displacing incidence points of the laser pulses on a surface of the glass or glass ceramic element thereof along the separation line; and subjecting the material of the glass or glass ceramic element located in a region of the portion to a phase transition so that the material contracts to detach the portion from the main part at the adjacently aligned filamentary damages along the separation line, while the main part remains intact as a whole.