For several decades, it was widely believed that a noninteracting disordered electronic system could only undergo an Anderson metal-insulator transition due to Anderson localization. However, numerous recent theoretical works have predicted the existence of a disorder-driven non-Anderson phase transition that differs from Anderson localization. The frustration lies in the fact that this non-Anderson disorder-driven transition has not yet been experimentally demonstrated in any system. Here, using angle-resolved photoemission spectroscopy, we present a case study of observing the non-Anderson disorder-driven transition by visualizing the electronic structure of the Weyl semimetal NdAlSi on surfaces with varying amounts of disorder. Our observations reveal that strong disorder can effectively suppress all surface states in the Weyl semimetal NdAlSi, including the topological surface Fermi arcs. This disappearance of surface Fermi arcs is associated with the vanishing of the topological invariant, indicating a quantum phase transition from a Weyl semimetal to a diffusive metal. These observations provide direct experimental evidence of the non-Anderson disorder-driven transition occurring in real quantum systems, a finding long anticipated by theoretical physicists.