We report magnetic susceptibility \chi, isothermal magnetization M, heat capacity C_p and electrical resistivity \rho measurements on undoped EuMn2As2 and K-doped Eu0.96K0.04Mn2As2 and Eu0.93K0.07Mn2As2 single crystals with the trigonal CaAl2Si2-type structure as a function of temperature T and magnetic field H. EuMn2As2 has an insulating ground state with an activation energy of 52 meV and exhibits antiferromagnetic (AFM) ordering of the Eu+2 spins S=7/2 at T_N1 = 15 K from C_p(T) and \chi(T) data with a likely spin-reorientation transition at T_N2 = 5.0 K. The Mn+2 3d5 spins-5/2 exhibit AFM ordering at T_N = 142 K from all three types of measurements. The M(H) isotherm and \chi(T) data indicate that the Eu AFM structure is both noncollinear and noncoplanar. The AFM structure of the Mn spins is also unclear. A 4% substitution of K for Eu in Eu0.96K0.04Mn2As2 is sufficient to induce a metallic ground state. Evidence is found for a difference in the AFM structure of the Eu moments in the metallic crystals from that of undoped EuMn2As2 versus both T and H. For metallic Eu0.96K0.04Mn2As2 and Eu0.93K0.07Mn2As2, an anomalous S-shape T dependence of \rho related to the Mn magnetism is found. Upon cooling from 200 K, \rho exhibits a strong negative curvature, reaches maximum positive slope at the Mn T_N ~ 150 K, and then continues to decrease but more slowly below T_N. This suggests that dynamic short-range AFM order of the Mn spins above the Mn T_N strongly suppresses the resistivity, contrary to the conventional decrease of \rho that is only observed upon cooling below T_N of an antiferromagnet.