Engineering muck (EM) is an underutilized construction waste rich in clay minerals. The mechanical properties, composition, microstructures and reaction mechanisms of various EM-based geopolymers produced via acid or alkali activation are comprehensively compared and discussed in this study. The results indicate that EM mainly contains clay minerals (kaolinite, halloysite and dioctahedral mica), feldspar and quartz. The geopolymerization reactivity of EM was improved following crushing and calcination pretreatments, which destroyed the microstructure of the clay minerals and formed a reactive amorphous phase. Acid activation of calcined EM (EM700°C) resulted in greater geopolymerization reactivity than alkali activation. The highest 7 and 28 day compressive strengths of phosphoric acid-activated EM-based geopolymers reached 27.31 and 24.37 MPa, respectively, under a water/binder mass ratio of 0.7 and an Al/P molar ratio of 0.9. Comparatively, the maximum 7 and 28 day compressive strengths of alkali-activated EM-based geopolymers were only 7.82 and 11.66 MPa, respectively, under a water/binder mass ratio of 0.6 and a SiO2/Na2O molar ratio of 1.75. For phosphoric acid activation, reactive Al3+ mainly from calcined clay (e.g. metakaolinite) in EM700°C geopolymerized with PO43– and silica, forming phosphate-containing phases and amorphous silico-aluminophosphate (SAP; Si–O–Al–O–P) gels. In contrast, reactive SiO2 and Al2O3 from EM700°C participated in the geopolymerization process in alkaline solution, forming sodium aluminosilicate hydrate (N–A–S–H) gels and the byproduct faujasite. The geopolymerization reactivity of EM700°C and the resulting composition variations in various solutions contributed to the differences in the compressive strengths of EM-based geopolymers. This study provides a theoretical basis for preparing acid/alkali-activated geopolymers from EM.