In this paper an observer for a class of uncertain mechanical systems, which are not necessarily bounded-input-bound-state, is proposed. The design technique presents a scheme in cascade, combining two methods: dissipativity and sliding-mode differentiation. The first uses the dissipative properties that the plant might have, ensuring that the error of the dissipative observer converges to some neighborhood of the origin. This allows to guarantee the use of a robust exact super-twisting based differentiator, providing theoretically exact finite-time convergence to the true states. The observer design is reduced to the solution of a matrix inequality, which could be transformed to a linear matrix inequality.