Mechanical testing of glass-fibre-reinforced composite (GFRP) plates made of twill fabric and a thermoplastic recyclable infusion resin is presented. The considered thermoplastic resin, ELIUM®, is made of poly-methylmethacrylate and can be infused with properly tuned vacuum techniques, in the same manner as all liquid resin. Tensile, flexural, and drop-dart impact tests were carried out to assess the mechanical properties of the composites considering different fabrication conditions, such as the different degassing pressure before infusion and three different infusion vacuum pressures. The work reports a methodology to infuse ELIUM resin at a relatively high vacuum pressure of 0.8 bar. X-ray microtomography analysis showed that the produced laminates are free of defects, differently from what was reported in the literature, where void problems related to a vacuum infusion pressure higher than 0.3–0.5 bar were pointed out. Vacuum pressure values influence the mechanical characteristics of the laminate: when higher vacuum pressures are adopted, the mechanical properties of the GFRP laminates are enhanced and higher values of elastic modulus and strength are obtained. On the other hand, degassing the resin before infusion does not influence the mechanical properties of the laminates. A maximum bending and tensile strength of 420 and 305 MPa were reached by using the vacuum infusion of 0.8 bar with an elastic modulus of 18.5 and 20.6 GPa, respectively. The density of the produced laminates increases at higher vacuum infusion pressure up to a maximum value of 1.81 g/cm3 with the fibre volume fraction of each laminate.