Among various grain refinement techniques, severe plastic deformation (SPD) has emerged as an effective method for enhancing material properties. As it involves a straightforward process of passing material through a die with a helical channel, twist extrusion (TE) is considered one of the simplest and most efficient techniques to induce shear strain. This study focuses on optimizing the critical TE processing parameters such as twist angle (β), coefficient of friction (τ), ram speed (V), and operating temperature (T) to improve outcomes for AA6063 alloy, targeting maximum load (P), net energy consumption (E), maximum strain (εmax), average strain (εavg) and strain inhomogeneity index (Ci). A Taguchi-based weighted grey relational analysis was used with an L16 orthogonal array, resulting in 16 simulation runs using DEFORM-3D software, which applies three-dimensional finite element modeling (FEM). The simulations used a billet with a 10 × 10 mm2 cross-sectional area. Weighted grey relational grade (GRG) values facilitated multi-objective optimization, and analysis of variance (ANOVA) determined the significance of each parameter. Results indicated that ‘τ’ is the most influential parameter with highest contribution of 59.01% for the GRG, whereas V and T have the least impact with lowest contribution percentages of 4.99 and 3.89% within the selected range. This approach offers a systematic framework for optimizing TE parameters to achieve improved material properties.