The alpha and beta relaxations are two fundamental processes in glass-forming materials, and quite important for many of the properties. Although intensive studies have found that alpha and beta relaxations can be tuned by changing the constituent elements, the underlying structural basis is still elusive. Here, we explored the effect of two key elements of Al and Ni on distinct beta and alpha relaxations in La65Al35 and La65Ni35 glass-forming alloys via classical and ab initio molecular dynamics simulations combined with dynamical mechanical spectroscopy. Unexpected coupling of relaxation in both beta and alpha relaxation time scales is observed for La and Al atoms in the La65Al35 system, which drastically suppresses the relaxation dynamics. It is revealed that the dynamic coupling of La and Al results from the covalent-like bonding interaction between Al atoms, which connect Al together, forming a network-like structure. The bonding network not only drastically slows down the dynamics of Al but also couples the motion of La and Al together. This finding elucidates the underlying basis of Al and Ni elements for distinct beta and alpha relaxation and sheds light on tuning the formation and properties of metallic glasses by minor alloying.