Precise control of emergent magnetic monopoles in artificial spin ice is pivotal for topological spin-based circuitry. We model a square-ice lattice on a “rotating squares” kirigami scaffold, so a single mechanical rotation angle $\theta$ reprograms dipolar couplings. Monte Carlo simulations and analytic results show $\theta$ not only drives a specific type of Dirac string tension through zero, reverses bound monopole motion, but also slows down and collimates the collective motion of multiple monopoles along nearly straight strings. The cut-and-fold design is based on a geometric principle that is inherently scale- and material-independent, offering a versatile route to reconfigurable ‘‘magnetricity’’ devices; the specific magnetic functionality, however, is determined by the chosen material and dimensions.

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• Dipolar interaction
• Frustrated magnetism
• Origami & Kirigami
• Artificial spin ice
• Metropolis algorithm
• Monte Carlo methods