The first data on target and beam-target asymmetries for the $gamma ptopi^0eta p$ reaction at photon energies from 1050 up to 1450 MeV are presented. The measurements were performed using the Crystal Ball and TAPS detector setup at the Glasgow tagged photon facility of the Mainz Microtron MAMI. The general assumption that the reaction is dominated by the $Delta 3/2^-$ amplitude is confirmed. The data are in particular sensitive to small contributions from other partial waves.