Due to a continuously developing population, our consumption of one of the most widely used building materials, concrete, has increased. The production of concrete involves the use of cement whose production is one of the main sources of CO2 emissions; therefore, a challenge for today’s society is to move towards a circular economy and develop building materials with a reduced environmental footprint. This study evaluates the possibility of using new sustainable supplementary cementitious materials (SCMs) from waste such as recycled concrete aggregates (RCAs) and mixed recycled aggregates (MRAs) from construction and demolition waste, as well as bottom ash from olive biomass (BBA-OL) and eucalyptus biomass ash (BBA-EU) derived from the production of electricity. A micronisation pre-treatment was carried out by mechanical methods to achieve a suitable fineness and increase the SCMs’ specific surface area. Subsequently, an advanced characterisation of the new SCMs was carried out, and the acquired properties of the new cements manufactured with 25% cement substitution in the new SCMs were analysed in terms of pozzolanicity, mechanical behaviour, expansion and setting time tests. The results obtained demonstrate the feasibility of using these materials, which present a composition with potentially reactive hydraulic or pozzolanic elements, as well as the physical properties (fineness and grain size) that are ideal for SCMs. This implies the development of new eco-cements with suitable properties for possible use in the construction industry while reducing CO2 emissions and the industry’s carbon footprint.