Aluminum extrusion is one of the most crucial processes in the production of structural and architectural profiles, where die durability directly affects both product quality and production costs. Extrusion dies operate under severe thermomechanical conditions, where the combined effect of high temperature and cyclic loading leads to significant damage of working surfaces. This study explores the dual role of tribological phenomena: enabling plastic deformation via high billet–die friction, while also triggering wear and damage that significantly reduce die service life. The analytical calculations investigate the mechanical behavior of two aluminum alloys, Al6063 and Al6082, during extrusion through a dies assembly consisting of a “hole–shaft” pair, made of H13 tool steel (a hot-working tool steel). Based on the structural loading scheme and extreme working parameters, the calculations compare the mechanical behavior of these alloys under acting extrusion force on the billet when forming two profiles at once. High pressures at calibration-zone induce die fatigue. The mechanical behavior of the billet is modeled through tribological formulation, where plastic flow is evaluated using the Johnson-Cook constitutive model. Analytical verification based on the Goodman fatigue criterion shows that, in both aluminum alloy cases, the dies operate under cyclic stress conditions. Additionally, working temperatures exceeding 0.4 Tm and long-term static loading give rise to creep strain. Although low in rate, this contributes significantly to the degradation process. The analytical findings will be supported and validated through numerical FEM analysis, aimed at identifying critical stress zones and proposing surface enhancement to extend die service life.