The new layered manganese oxychalcogenides (LaO)$_2$Mn$_2$Se$_2$O and (BaF)$_2$Mn$_2$Se$_2$O, isostructural to (LaO)$_2$Fe$_2$Se$_2$O, were synthesized by using solid state reaction. The single crystals of former compound were also successfully grown by using high temperature fusion method. The polycrytalline samples showed the insulating behavior, with the activation energy gaps of about 278 meV and 416 meV for (LaO)$_2$Mn$_2$Se$_2$O and (BaF)$_2$Mn$_2$Se$_2$O, respectively. The magnetic susceptibility indicated an antiferromagnetic (AFM) transition at around 160K and strong anisotropic magnetic properties below T$_N$ for the former compound, which suggests a long-range canted AFM ordering. A broad maximum of the susceptibility can be observed for the two compound at high temperatures, say 360 K and 210 K respectively, suggesting that strong magnetic correlation gives rise to low-dimensional AFM or short-range ordering at high temperatures in these rare transition metal oxychalcogenides with a frustrated AFM checkerboard spin lattice.