Here we report the evolution of structural, magnetic, and transport properties in MnBi2-xSbxTe4 (0 <= x <= 2) single crystals. MnSb2Te4, isostructural to MnBi2Te4, is successfully synthesized in single-crystal form. Magnetic measurements suggest an antiferromagnetic order below T-N = 19 K for MnSb2Te4 with the magnetic moments aligned along the crystallographic c axis. With increasing Sb content in MnBi2-xSbxTe4, the a-lattice parameter decreases linearly following Vegard's law, while the c-lattice parameter shows little compositional dependence. The contraction along a is caused by the reduction of the Mn-Te-Mn bond angle, while the Mn-Te bond length remains nearly constant. The antiferromagnetic ordering temperature slightly decreases from 24 K for MnBi2Te4 to 19 K for MnSb2Te4. More dramatic change was observed for the critical magnetic fields required for the spin-flop transition and the moment saturation. Both critical fields decrease with increasing Sb content for x <= 1.72; a spin-flip transition occurs in MnSb2Te4 at a small field of 3 kOe applied along the c axis. In high magnetic fields, the saturation moment at 2 K shows significant suppression from 3.56 mu(B)/Mn for MnBi2Te4 to 1.57 mu(B)/Mn for MnSb2Te4. Analysis of the magnetization data suggests that both the interlayer magnetic interaction and single-ion anisotropy decrease with increasing Sb content for x <= 1.72. The partial substitution of Bi by Sb also dramatically affects the transport properties. A crossover from n-type to p-type conducting behavior is observed around x approximate to 0.63. Our results show close correlation between structural, magnetic, and transport properties in MnBi2-xSbxTe4 and that partial substitution of Bi by Sb is an effective approach to fine tuning both the magnetism and transport properties of MnBi2-xSbxTe4.