This study analysed the fine particle (<5 mm) waste generated during siliceous or calcareous (depending on the composition of the original aggregate) concrete waste crushing. In the absence of industrial applications, such waste is amassed in open-air stockpiles on construction and demolition wastes (CDW) management plant grounds. The aim pursued was to find an outlet for that material in the cement industry. The starting waste, sourced from six Spanish management facilities, was characterised for its chemical and mineralogical composition, physical properties and pozzolanicity. The mineralogical phases in the CDW/lime system and their variations during the pozzolanic reaction were likewise identified. The findings showed that the fine waste consisted primarily in quartz, calcite, micas and feldspars, with smaller fractions of kaolinite and cement anhydrous phases. No portland cement hydration phases were identified. All six types analysed exhibited medium to low pozzolanicity, with the highest values recorded for the siliceous waste. Ettringite, C–S–H gels and calcium aluminate hydrates (C4AH13, C4AcH12) were identified during the pozzolanic reaction in CDW/lime system. Therefore, this type of waste can be reused as supplementary cementitious material with low-medium pozzolanic activity.