This paper examines the performance of multi-binder conventional geopolymer mixes (GCMs) with relatively high early strength, achieved through curing at ambient temperature. Mixes incorporating ground granulated blast-furnace slag (GGBS), fly ash (FA) and microsilica (MS) and sodium metasilicate anhydrous, were assessed in terms of workability, mechanical properties and embodied carbon. A cement mortar was also prepared for the sake of comparison. The best performing GCM was then used as a reference for rubberised geopolymer mixes (RuGM) in which the mineral aggregates were replaced by recycled rubber particles in proportions up to 30% by volume. Experimental results were combined with embodied carbon estimations in a multi-criteria assessment to evaluate the performance of each material. A mix with a 75/25 GGBS-to-FA ratio, in which 5% MS was added, had the best performance in terms of strength, workability, water absorption and environmental impact. The compressive strength was above 50 MPa, similar to that of the cement mortar. The latter had significantly higher embodied carbon, with factors ranging between 3.48 to 4.20, compared with the CGM mixes. The presence of rubber particles reduced the mechanical properties of RuGM proportionally with the rubber amount, but had similar workability and embodied carbon to CGMs. Finally, a strength degradation model is validated against the tests from this paper and literature to estimate the compressive strength of RuGM, providing reliable predictions over a wide range of rubber contents.