Tidal turbines experience large load fluctuations due to the unsteady environment and the shear in the tidal flow. Mitigating these fluctuations without affecting the mean load would result in lower capital and operational costs. In this paper we discuss how this could be achieved through blades that passively and elastically adapt their camber and angle of attack to counteract unsteady flow conditions. Firstly, we discuss the underlying principles of unsteady thrust mitigation. We show that complete cancellation of the thrust fluctuations would be possible if every blade section could pitch passively and independently of neighbouring sections. Secondly, we provide proof of principle for two practical implementations through physical experiments and computational fluid dynamics simulations. We consider a blade that is rigid near the leading edge and flexible near the trailing edge. We show that the unsteady load mitigation is proportional to the ratio between the length of the flexible and rigid parts of the blade. For example, for a blade section where the flexibility is concentrated in a hinge at 3/4 of the chord, the amplitude of the fluctuations is 3/4 of the original amplitude. Secondly, we consider a solid, rigid blade with a passive pitch mechanism. We show that, for a 1 MW turbine operating in shear flow, more than 80% of the unsteady loading is mitigated. These results demonstrate the potential effectiveness of morphing blades for mitigating thrust fluctuations on tidal turbines.