In this paper, we conduct the experiment and simulation on 31D_5/2+6S_1/2(F = 4) Cs₂ ultralong-range Rydberg molecules (ULRMs). These molecules are prepared by employing a two-photon photoassociation scheme. Two distinct ultralong-range Rydberg molecular signals are observed at the detuning –162.8 MHz and –66.6 MHz of 31D_5/2 atomic resonant line, which are bound by the pure triplet potential and mixed singlet-triplet potential, respectively. We use the model of scattering interaction between the Rydberg electron and ground-state atom to perform the simulation. The molecular potential-energy curves are obtained by solving the Hamiltonian on a grid of intermolecular distances R. The calculations of the binding energy of pure triplet and mixed singlet-triplet v = 0 vibrational states are compared with the experimental measurements. The calculated and measured values of the binding energy are in good agreement. The s-wave pure triplet and singlet zero-energy scattering length are obtained to be a_\rms^\rmT(0)=-19.16a_0 and a_\rms^\rmS(0)=-1.92a_0 , respectively. This kind of molecule with large size, abundant vibrational states and large permanent electric dipole moment is an excellent candidate for studying low-energy collision dynamics. The study of these molecules will further deepen and enrich the understanding of the special binding mechanism and exotic properties of the ULRMs.