We propose a semantic shape editing method to edit 3D triangle meshes using parametric implicit surface templates, benefiting from the many advantages offered by analytical implicit representations, such as infinite resolution and boolean or blending operations. We propose first a template fitting method to optimize its parameters to best capture the input mesh. For subsequent template edits, our novel mesh deformation method allows tracking the template's 0-set even when featuring anisotropic stretch and/or local volume change. We make few assumptions on the template implicit fields and only strictly require continuity. We demonstrate applications to interactive semantic shape editing and semantic mesh retargeting.