  Spin-ordered states close to metal-insulator transitions are poorly
understood theoretically and challenging to probe in experiments. Here, we
propose that the quantum twisting microscope, which provides direct access to
the energy-momentum resolved spectrum of single-particle and collective
excitations, can be used as a novel tool to distinguish between different types
of magnetic order. To this end, we calculate the single-particle spectral
function and the dynamical spin-structure factor for both a ferromagnetic and
antiferromagnetic generalized Wigner crystal formed in fractionally filled
moir\'e superlattices of transition metal dichalcogenide heterostructures. We
demonstrate that magnetic order can be clearly identified in these response
functions. Furthermore, we explore signatures of quantum phase transitions in
the quantum twisting microscope response. We focus on the specific case of
triangular moir\'e lattices at half filling, which have been proposed to host a
topological phase transition between a chiral spin liquid and a 120 degree
ordered state. Our work demonstrates the potential for quantum twisting
microscopes to characterize quantum magnetism in moir\'e heterostructures.
