We present mechanically strong and self-healable clay hydrogels containing 2-8 w/v % ds-DNA together with a synthetic biocompatible polymer, poly(N,N-dimethylacrylasnide). Clay nanoparticles in the hydrogels act like a chemical cross-linker and promote their elastic behavior, whereas DNA contributes to their viscoelastic energy dissipation. The extent of mechanical hysteresis during cyclic tensile tests reveals that the strength of intermolecular bonds in DNA/clay hydrogels is in the range of the strength of hydrogen bonds. The hydrogels exhibit a high stretchability (up to 1500%) and a tensile strength between 20 and 150 kPa. They have the ability to self-heal, which is induced by heating the damaged gel samples above the melting temperature of ds-DNA. When comparing the mechanical properties of the hydrogels before and after healing, the healing efficiency is greater than 100%. We also demonstrate that ds-DNA molecules entrapped in the gel network undergoes thermal denaturation/renaturation cycles, leading to a further improvement in the mechanical properties of the hydrogels.