This study examines the impact of three factors on the tensile and compressive behaviour of 3D-printed parts: (1) the addition of short carbon fibres to the nylon filament used for 3D printing, (2) the infill pattern, and (3) the speed at which the materials are strained during testing. The results show that adding carbon fibres to the nylon filament reduces variability between tests and emphasises the effect of print orientation. When the infill pattern is aligned with the direction of loading, the tensile strength of all samples increases, with the largest increase of 100% observed in the carbon fibre-reinforced samples, compared to a 37% increase in the strength of nylon samples. The carbon fibre-reinforced samples are also highly dependent on strain rate, with a 60% increase in tensile strength observed at a faster testing speed of 300 mm/min (9 min−1) compared to 5 mm/min (15 min−1). Nylon samples show a decrease of approximately 10% in tensile strength at the same increased speed. The compressive strength of the composite samples increases by up to 130% when the print path is parallel to the loading direction. Increases of up to 50% are observed in the compressive modulus of the composite samples at a test speed of 255 mm/min (9 min−1) compared to 1.3 mm/min (0.05 min−1). Similar trends are not seen in pure nylon samples. This study is the first to report on the variation of Poisson’s ratio of short carbon fibre-reinforced 3D-printed parts. The results show increases of up to 34% and 76% in the tensile and compressive Poisson’s ratios, respectively, when printing parameters are altered. The findings from this research will contribute to the design and numerical modelling of 3D-printed composites.