Additively manufactured (AM) metallic materials commonly possess substantial microscale internal stresses that manifest as intergranular and intragranular residual stresses. However, the impact of these residual stresses on the mechanical behaviour of AM materials remains unexplored. Here we combine in situ synchrotron X-ray diffraction experiments and computational modelling to quantify the lattice strains in different families of grains with specific orientations and associated intergranular residual stresses in an AM 316L stainless steel under uniaxial tension. We measure pronounced tension-compression asymmetries in yield strength and work hardening for as-printed stainless steel, and show they are associated with back stresses originating from heterogeneous dislocation distributions and resultant intragranular residual stresses. We further report that heat treatment relieves microscale residual stresses, thereby reducing the tension-compression asymmetries and altering work-hardening behaviour. This work establishes the mechanistic connections between the microscale residual stresses and mechanical behaviour of AM stainless steel.