Mix-cumulants of conserved charge distributions are sensitive observables for probing properties of the QCD medium and phase transition in heavy-ion collisions.To perform precise measurements,efficiency correction is one of the most important step.In this study,using the binomial efficiency model,we derive efficiency correction formulas for mutually exclusive and inclusive variables.The UrQMD model is applied to verify the validity of these formulas for different types of correlations.Furthermore,we investigate the effect of the multiplicity loss and con-tamination emerging from the particle identifications.This study provides important steps toward future measure-ments of mixed-cumulants in relativistic heavy-ion collisions.