This work introduces a distributed memory machine and octree-based Finite Element (FE) framework for modeling metal Additive Manufacturing (AM) processes. In this sense, an Adaptive Mesh Refinement (AMR) is used to accurately capture the complex geometrical domain and the physical phenomena of AM processes for the part-scale analysis. AMR is used in conjunction with refinement criteria suitable for this problem: (1) a geometric criterion for refining the material deposition path, and (2) an accuracy criterion based on an a-posteriori error-indicator of the displacement field. As a consequence, the geometry and numerical solution are accurately captured whilst the number of FEs is kept controlled along the simulation. Numerical simulations involving growing domains are presented to assess the accuracy and computational efficiency of the framework with different octree-based and structured fixed mesh configurations. The overall performance of the framework is evaluated through a strong scalability analysis to track the evolution of the computational time along the simulation, where all steps composing the AM pipeline are independently analyzed. The strong scalability test consists of a discrete evolving domain with over 15 M active nodes, solved on a High-Performance Computer (HPC) using 2, 048 processors.