We report the physical properties of Tb2Hf2O7 based on ac magnetic susceptibility χac(T), dc magnetic susceptibility χ(T), isothermal magnetization M(H), and heat capacity Cp(T) measurements combined with muon spin relaxation (μSR) and neutron powder diffraction measurements. No evidence for long-range magnetic order is found down to 0.1 K. However, χac(T) data present a frequency-dependent broad peak (near 0.9 K at 16 Hz) indicating slow spin dynamics. The slow spin dynamics is further evidenced from the μSR data (characterized by a stretched exponential behavior) which show persistent spin fluctuations down to 0.3 K. The neutron powder diffraction data collected at 0.1 K show a broad peak of magnetic origin (diffuse scattering) but no magnetic Bragg peaks. The analysis of the diffuse scattering data reveals a dominant antiferromagnetic interaction in agreement with the negative Weiss temperature. The absence of long-range magnetic order and the presence of slow spin dynamics and persistent spin fluctuations together reflect a dynamical ground state in Tb2Hf2O7.