Metal organic magnets have enormous potential to host a variety of electronic and magnetic phases that originate from a strong interplay between the spin, orbital, and lattice degrees of freedom. We control this interplay in the quantum magnet CuF₂(D₂O)₂(pyz) by using high pressure to drive the system through structural and magnetic phase transitions. Using neutron scattering, we show that the low pressure state, which hosts a two-dimensional square lattice with spin-wave excitations and a dominant exchange coupling of 0.89 meV, transforms at high pressure into a one-dimensional spin chain hallmarked by a spinon continuum and a reduced exchange interaction of 0.43 meV. This direct microscopic observation of a magnetic dimensional crossover as a function of pressure opens up new possibilities for studying the evolution of fractionalised excitations in low-dimensional quantum magnets and eventually pressure-controlled metal-insulator transitions.