Graphene-like two-dimensional (2D) silicon carbide or siligraphene has attracted remarkable attention, owing to its fascinating physical properties. Nevertheless, the first high-quality siligraphene, i.e. monolayer Si₉C₁₅, was synthesised very recently, which exhibits an excellent semiconducting behaviour. In this work, we investigate the mechanical properties of Si₉C₁₅ siligraphene by using atomistic simulations including density functional theory (DFT) calculations and molecular dynamics (MD) simulations. Both methods confirm the existence of intrinsic negative Poisson's ratios in Si₉C₁₅ siligraphene, which, as illustrated by MD simulations, is attributed to the tension-induced de-wrinkling behaviours of its intrinsic rippled configuration. Different de-wrinkling behaviours are observed in different directions of Si₉C₁₅ siligraphene, which result in the anisotropy of its auxetic properties. The fracture properties of Si₉C₁₅ siligraphene are similarly anisotropic, but relatively large fracture strains are observed in different orientations, indicating the stretchability of Si₉C₁₅ siligraphene. The stretchability together with the strain-sensitive bandgap of Si₉C₁₅ siligraphene observed in DFT calculations indicates the effectiveness of strain engineering in modulating its electronic properties. The combination of unique auxetic properties, excellent mechanical properties and tunable electronic properties may make Si₉C₁₅ siligraphene a novel 2D material with multifunctional applications.