The objective of this study is to investigate the performance of normal- and high-strength concretes including limestone powder (LP) through their mechanical properties. Moreover, sustainable flat plates made of these concretes were investigated through their punching strength. For this purpose, two different types of concrete (normal- and high-strength) with various limestone replacement ratios of 0%, 5%, 15%, and 20% by weight were designed. The fresh and hardened characteristics of the mixtures were investigated at various ages. By this means, the experimental behavior of reinforced concrete (RC) flat plate slabs made with limestone powder subjected to punching shear failure was studied. Slump value increased up to a 5% replacement of LP; after that, there was a tendency for the slump value to decrease as the replacement of limestone in normal-strength LP concrete increased. However, slump values for high-strength LP concrete increased as the LP replacement amount increased. There was a steady decrease in the compressive strength and splitting tensile strength values with the increase in LP content in normal concrete. However, in the high-strength LP concrete, with more than 10% of replacement LP, a decrease in the compressive strength values and splitting tensile strength values occurred. Compared to the control slab specimen without LP, in normal strength, the slab specimens with LP exhibit a larger ultimate shear load for slab specimens containing 5% and 10% of LP. The maximum increment for RC slabs containing 10% limestone powder was 3.8%. However, in high-strength concrete, the slab specimens with LP remained at the same ultimate shear load as control slabs, up to 10% of LP. high-strength concrete slabs with 5–20% LP showed an overall increase of (17.2%) in punching strength over the corresponding LP normal-strength concrete slabs. The corresponding increase for control slabs was 18.8%. It can be concluded that introducing LP improves the slab punching strength in a similar way that is found in non-sustainable slabs when using either normal- or high-strength concrete.