Laser cutters take vector data for the shapes they cut or engrave as input, however, re-using a given design with different material or on a different machine requires adaptation of the template. Unfortunately, vector drawings lack the semantic information required for an automated adjustment to new parameters, making the manual adjustment a tedious and error-prone process for end-users. We present LaserSVG, a standard-compliant vector-based file format, software library, and authoring tool to specify, generate, exchange and re-use responsive laser-cutting templates. With LaserSVG, designers can easily turn their vector-drawings into parametric templates that end-users can easily adjust to new materials or production parameters. Our tools provide various functions for parametric design that allows end-users and designers to adapt objects while ensuring overall consistency of the results.