Cutting torch guide structures, systems, and kits include a base structure having a bottom surface and a channel formed in the base structure, a mechanically switched permanent magnet coupled to the base structure and configured to mechanically switch between two magnetic states, and a cutting torch guide structure configured to be releasably received in the channel and magnetically coupled to the base structure by magnetic attraction between a at least one permanent magnet fixed in at least one recess in the channel and a guide structure permanent magnet fixed to the cutting torch guide structure, where the cutting torch guide structure is configured with a first portion that is removable received in the channel of the base structure and a second portion that overhangs the base structure and includes an edge that defines a predefined shape and is configured to be in slidable contact with a cutting torch tip.