Two methods for the extraction of Stress Intensity Factors (SIFs) from three-dimensional (3-D) problems are presented: the Contour Integral Method and the Cutoff Function Method. The formulations are tailored for the Generalized Finite Element Method and mixed-mode 3-D propagating cracks. The case of crack faces loaded by prescribed tractions is also considered. Another contribution of this paper is a procedure to control the noise of extracted SIFs based on the Moving Least Squares Method. The proposed approach provides a continuous and smooth approximation of 3-D SIF functions for each fracture mode. Numerical experiments demonstrating the accuracy and robustness of the proposed methodology are presented. They include 3-D mixed-mode fatigue crack growth simulations and the case of a pressurized crack.