Based on the M4-square-containing M4Li2 (M = Al, Ga, In, Tl, Ge, Sn, Pb, Sb, Bi, Cu, Ag, Au, and Hg) clusters, we computationally designed two-dimensional (2D) M2Li sheets consisting of M4-square motifs. The four M2Li-I (M = Sb, Bi, Ag, and Au) monolayers with Li square sublayer sandwiched between two M square sublayers (P4/mmm space group) were confirmed to be stable (high cohesive energies, positive vibrational frequencies, moderate Young's moduli, and structural integrity during first-principles molecular dynamics simulations at 500 K), and the particle swarm optimization (PSO) method identified these constructed monolayers as the global minima in the 2D space. The three M2Li-I (M = Sb, Bi, and Ag) monolayers demonstrated a half-auxetic behavior. Ag2Li-I could well activate CO2 and convert it into HCOOH by following the path * → *CO2 → *OCHO → *HCOOH → *+HCOOH. Particularly, Ag2Li-I shows great promise as an electrocatalyst for CO2 reduction as its limiting potential is as low as 0.40 (0.27) V without (with) considering the solvent effect. Our theoretical explorations reveal that lithium can stabilize the square metal monolayers, and the stable square binary metal sheets exhibit diverse mechanical and electrochemical properties, which can be used in the fields of mechanics and electrochemical catalysis.