Few systematic studies on the correlation between alloy microstructure and mechanical failure of the AlSi10Mg alloy produced by laser-based powder bed fusion (L-PBF) are available in the literature. This work investigates the fracture mechanisms of the L-PBF AlSi10Mg alloy in as-built (AB) condition and after three different heat treatments (T5 (4 h at 160 °C), standard T6 (T6B) (1 h at 540 °C followed by 4 h at 160 °C), and rapid T6 (T6R) (10 min at 510 °C followed by 6 h at 160 °C)). In-situ tensile tests were conducted with scanning electron microscopy combined with electron backscattering diffraction. In all samples the crack nucleation was at defects. In AB and T5, the interconnected Si network fostered damage at low strain due to the formation of voids and the fragmentation of the Si phase. T6 heat treatment (T6B and T6R) formed a discrete globular Si morphology with less stress concentration, which delayed the void nucleation and growth in the Al matrix. The analysis empirically confirmed the higher ductility of the T6 microstructure than that of the AB and T5, highlighting the positive effects on the mechanical performance of the more homogeneous distribution of finer Si particles in T6R.