  We study the zero-temperature phase diagram and the low-energy excitations of
a mixed-spin ($S_1>S_2$) $J_1-J_2$ Heisenberg model defined on a square lattice
by using a spin-wave analysis, the coupled cluster method, and the Lanczos
exact-diagonalization technique. As a function of the frustration parameter
$J_2/J_1$ ($ >0$), the phase diagram exhibits a quantized ferrimagnetic phase,
a canted spin phase, and a mixed-spin collinear phase. The presented results
point towards a strong disordering effect of the frustration and quantum spin
fluctuations in the vicinity of the classical spin-flop transition. In the
extreme quantum system $(S_1,S_2)=(1,{1/2})$, we find indications of a new
quantum spin state in the region $0.46< J_2/J_1<0.5$
