Both Sb2S3 and Sb2Se3 have been studied as promising photocatalytic and photovoltaic semiconductors because of their suitable bandgaps, high light absorption coefficients and good stability. Through forming the mixed-anion Sb2(S,Se)3 alloys, the bandgaps and lattice parameters can be tuned and a band structure engineering design of semiconductor heterostructures becomes possible. However, the properties of the disordered Sb2(S,Se)3 alloys are currently not clear. Using first-principles calculations, we show that the alloys are highly miscible with low formation enthalpies, so composition-variable and uniform alloys can be fabricated under room temperature. The bandgaps of the alloys change almost linearly as the alloy composition (S/Se ratio) varies, indicating that the bandgap engineering can be quite flexible. The calculations of the defect properties show that there are dozens of detrimental defects producing deep levels in the bandgap of the alloy under the Sb-rich (Se-poor) condition, which can cause serious electron-hole non-radiative recombination and limit the minority carrier lifetime. The formation of these detrimental defects can be largely suppressed under the Sb-poor condition, so we propose that the Sb-poor (Se-rich) condition should be adopted for fabricating Sb2(S,Se)3 alloys as photocatalytic and photovoltaic light-absorber semiconductors with long minority carrier lifetimes.