  Square-net-layered materials have attracted attention as an extended research
platform of Dirac fermions and of exotic magneto-transport phenomena. In this
study, we investigated the magneto-transport properties of LaAgSb$_2$, which
has Sb-square-net layers and shows charge density wave (CDW) transitions at
ambient pressure. The application of pressure suppresses the CDWs, and above a
pressure of 3.2 GPa, a disordered phase with no CDWs is realized. By utilizing
a mechanical rotator combined with a high-pressure cell, we observed the
angular dependence of the Shubnikov-de Haas (SdH) oscillation up to 3.5 GPa and
confirmed the notable two-dimensional nature of the Fermi surface. In the
disordered phase, we also observed a remarkable field-angular-dependent
magnetoresistance (MR), which exhibited a "butterfly-like" polar pattern. To
understand these results, we theoretically calculated the Fermi surface and
conductivity tensor at the disordered phase. We showed that the SdH frequency
and Hall coefficient calculated based on the present Fermi surface model agree
well with the experiment. The transport properties in the disordered phase are
mostly dominated by the anisotropic Dirac band, which has the highest
conductivity owing to linear energy dispersions. We also proposed that
momentum-dependent relaxation time plays an important role in the large
transverse MR and negative longitudinal MR in the disordered phase, which is
experimentally supported by the considerable violation of Kohler's scaling
rule. Although quantitatively complete reproduction was not achieved, the
calculation showed that the elemental features of the butterfly MR could be
reasonably explained as the geometrical effect of the Fermi surface.
