The influence of four naturally occurring mineral additives (zeolite, diatomite, trass and bentonite) on the hydration and properties of cement pastes and mortars was investigated. The materials change the phase composition, heat of hydration (determined by calorimetry) and mechanical properties of composites. After 28 days, the amount of Ca(OH)2 was reduced by up to 23% and up to 35% more C-S-H was formed, as proved by TG measurements. Differences were observed in the kinetics of heat release, especially for 25% of the addition. In the calorimetric curves, an additional exothermic effect is observed, related to the alteration in the hydration of C3A in cement. From the point of view of beneficial influence on mechanical properties of mortars, the additives could be ranked as follows: bentonite < diatomite, zeolite < trass after 2 days and bentonite < diatomite < trass < zeolite after 28 days of curing. The highest compressive strength (58.5 MPa) was observed for the sample with a 10% addition of zeolite. Zeolite, trass, bentonite and diatomite are all pozzolanic materials; however, their activity varies to an extent due to the differences in their specific surface area and the content of the amorphous phase, responsible for the pozzolanic reaction.