The effect of 50\% Cu doping at the Au site in the topological Dirac semimetal CaAuAs is investigated through electronic band structure calculations, electrical resistivity, and magnetotransport measurements. Electronic structure calculations a suggest broken-symmetry-driven topological phase transition from the Dirac to triple-point state in CaAuAs via alloy engineering. The electrical resistivity of both the CaAuAs and CaAu$_{0.5}$Cu$_{0.5}$As compounds shows metallic behavior. Nonsaturating quasilinear magnetoresistance (MR) behavior is observed in CaAuAs. On the other hand, MR of the doped compound shows a pronounced cusplike feature in the low-field regime. Such behavior of MR in CaAu$_{0.5}$Cu$_{0.5}$As is attributed to the weak antilocalization (WAL) effect. The WAL effect is analyzed using different theoretical models, including the semiclassical $\sim\sqrt{B}$ one which accounts for the three-dimensional WAL and modified Hikami-Larkin-Nagaoka model. Strong WAL effect is also observed in the longitudinal MR, which is well described by the generalized Altshuler-Aronov model. Our study suggests that the WAL effect originates from weak disorder and the spin-orbit coupled bulk state. Interestingly, we have also observed the signature of chiral anomaly in longitudinal MR, when both current and field are applied along the $c$ axis. The Hall resistivity measurements indicate that the charge conduction mechanism in these compounds is dominated by the holes with a concentration $\sim$10$^{20}$ cm$^{-3}$ and mobility $\sim 10^2$ cm$^2$ V$^{-1}$ S$^{-1}$.