Two-component epoxy-based adhesives are frequently used to bond metals and composite materials in structural lightweight applications. Due to the significant nonlinearity in the joints’ constitutive equations and the complex shapes of the adherents, numerical techniques such as the finite element method (FEM) are the preferred method for strength assessment. This work presents an experimental approach for determining the mechanical response of a two-component epoxy adhesive by means of a multilinear elastoplastic material definition. The tensile behavior was established by conducting static tensile tests using a total of 72 adhesive bulk samples, and the resulting stress–strain curves are approximated using multiple regression lines. The adhesive's high viscosity caused inhomogeneities in the adhesive bulk, which were detected on the fracture surfaces of the samples. By excluding samples with air inclusions larger than 100 µm from the analysis, the scatter in the results is reduced to an acceptable level. Assuming isotropic material behavior, the mechanical response of the adhesive is fully characterized by additionally determining the shear modulus. This is done through torsion testing of additively manufactured butt-bonded cylinders. The design of the test sample failed to sufficiently account for the chemical shrinkage of the adhesive, resulting in frictional effects between the integrated adhesive fill gap spacers during test execution. Additionally, the high stiffness of the adhesive layer is underestimated, which negatively impacted the measurement resolution of the torsional angle. Consequently, the shear modulus values obtained exhibited an unacceptable level of scattering.