Using molecular dynamics simulation, we have studied the low-energy sputtering at the energies near the sputtering threshold. Different projectile-target combinations of noble metal atoms (Cu, Ag, Au, Ni, Pd, and Pt) are simulated in the range of incident energy from 0.1 to 200 eV. It is found that the threshold energies for sputtering are different for the cases of M1 < M2 and M1 ≥ M2, where M1 and M2 are atomic mass of projectile and target atoms, respectively. The sputtering yields are found to have a linear dependence on the reduced incident energy, but the dependence behaviors are different for the both cases. The two new formulas are suggested to describe the energy dependences of the both cases by fitting the simulation results with the determined threshold energies. With the study on the energy dependences of sticking probabilities and traces of the projectiles and recoils, we propose two different mechanisms to describe the sputtering behavior of low-energy atoms near the threshold energy for the cases of M1 < M2 and M1 ≥ M2, respectively.