A cluster of N ligand-receptor pairs between two parallel surfaces under an applied force F=Γt with a constant loading rate Γ is considered. Our theoretical and numerical studies show that there is a characteristic force f(c) and a characteristic loading rate Γ(c). At Γ<Γ(c), the mean rupture force F(r) of the cluster is close to but lower than Nf(c). In this regime, cluster dissociation can be modeled as a one-dimensional barrier crossing process and F(r) scales like Nf(c)-F(r)~N(1/3)[ln(Γ(c)/Γ)](2/3). At Γ=Γ(c), the cluster dissociation occurs at F(r)=Nf(c). At Γ>Γ(c), F(r) for clusters with large N is well predicted by the rate equation because the fluctuations of the number of closed bonds are unimportant. Our study shows that f(c) and Γ(c) are important emergent properties for understanding the mechanical response of adhesion clusters.