By using the Hartree-Fock-Bogoliubov approximation of mean-field theory and the analytic method based on Thomas-Feimi approximation, the Landau damping and frequency-shift of (0, 0, 2) scissors mode in a disc-shaped Bose-Einstein condensate are investigated and the damping rate and frequency-shift magnitude as well as their temperature dependence are calculated. In the calculation, the practical relaxations of the elementary excitations and the orthometric relation among the relaxations are considered in the relation for the perturbed eigenfrequency of mean-field theory to obtain the calculation formula of damping and frequency-shift, and the first-order approximation of Gaussian distribution function is employed for the ground-state wavefunction to eliminate the divergence of the three-mode coupling matrix elements in Thomas-Fermi approximation. Taking the same parameters of particle number, trapping frequency and anisotropy as those in relevent experiment research, our theoretical calculation results accord with the relevent experimental measurement results. Because of the complexity of the theory and the difficulty of calculation, most of mean-field theory researches on damping and frequency shift of collective excitation in one and two component Bose-Einstein condensates adopt semi-classical approximation, the quasi-particle excitation spectrum is regarded as continuously integrating each quasi-particle transition contribution to damping and frequency shift. In this paper, the damping and frequency shift are calculated according to the discrete quasi-particle excitation spectrum, and in the course of the study the improving of method of considering the practical relaxations of the elementary excitations and the orthometric relation among the relaxations is put forward. It is hoped that the method will have some reference value in the future work.