The heat transport mechanism has an engrossing application in effective heat management for the automobile industry and the biomedical industry. The analysis of the MHD graphene−carboxymethyl cellulose (CMC) solution−water nanofluid past a stretchable wall with Joule heating and velocity slip impact is performed in this regard. A graphene-based nanofluid is considered. The dynamic model is used to simplify the complicated ordinary differential equations into non-dimensional forms, which are then evaluated analytically. Numerical data and graphs are produced to analyze the consequences of a physical entity with the aid of Maple 17. Moreover, the velocity field is decreased, while the magnitude of the magnetic parameter is increased. A decrease in θ(η) is observed as a result of an increase in ϕ. It is noted that a rise in the magnetic parameter causes a fall in the temperature distribution. It is perceived that −f′′(0) is decreased with an augmentation in βs, and an opposite trend is shown for ϕ. The velocity profile is the growing function of Mgn, βs, and Kve, with the reversed mode shown in case of ϕ. The temperature profile is the declining function of Pr, Ecrt, ϕ, and χ, with a contradictory trend observed for Mgn and βs. The flow regime is displayed against the viscoelastic parameter.