The Abrasion–Ablation Monte Carlo for Colliders (AAMCC) model is used to study the characteristics of spectator matter in central collisions of relativistic 238 U nuclei, which are sensitive to the mutual orientation and the degree of deformation of the colliding nuclei. It is shown that the multiplicity of spectator neutrons and their forward-backward asymmetry substantially depend on the initial mutual orientation of 238 U nuclei, which makes it possible to separate tip-body events with a high forward-backward asymmetry and a maximum multiplicity of spectator neutrons, as well as side-side events with a similar multiplicity, but with a minimal asymmetry. It is found that an increase in the quadrupole deformation parameter of 238 U nuclei leads to a proportional increase in the multiplicity of spectator neutrons in tip-body events. Thus, the detection of spectator neutrons in collisions of relativistic deformed nuclei in an experiment can be used to study a degree of their deformation and to select collisions of a certain orientation.