Graphene foam (GF), a 3‐dimensional derivative of graphene, has received much attention recently for applications in tissue engineering due to its unique mechanical, electrical, and thermal properties. Although GF is an appealing material for cartilage tissue engineering, the mechanical properties of GF‐tissue composites under dynamic compressive loads have not yet been reported. The objective of this study is to measure the elastic and viscoelastic properties of GF and GF‐tissue composites under unconfined compression when quasi‐static and dynamic loads are applied at strain magnitudes below 20%. The mechanical tests demonstrate a 46% increase in the elastic modulus and a 29% increase in the equilibrium modulus after 28‐days of cell culture as compared to GF soaked in tissue culture medium for 24 h. There is no significant difference in the amount of stress relaxation, however, the phase shift demonstrates a significant increase between pure GF and GF that has been soaked in tissue culture medium for 24 h. Furthermore, the authors have shown that ATDC5 chondrocyte progenitor cells are viable on graphene foam and have identified the cellular contribution to the mechanical strength and viscoelastic properties of GF‐tissue composites, with important implications for cartilage tissue engineering.