Taking advantage of quantum mechanics for executing computational tasks faster than classical computers(1) or performing measurements with precision exceeding the classical limit(2,3) requires the generation of specific large and complex quantum states. In this context, cluster states(4) are particularly interesting because they can enable the realization of universal quantum computers by means of a 'one-way' scheme(5), where processing is performed through measurements(6). The generation of cluster states based on sub-systems that have more than two dimensions, d-level cluster states, provides increased quantum resources while keeping the number of parties constant(7), and also enables novel algorithms(8). Here, we experimentally realize, characterize and test the noise sensitivity of three-level, four-partite cluster states formed by two photons in the time(9) and frequency(10) domain, confirming genuine multi-partite entanglement with higher noise robustness compared to conventional two-level cluster states(6,11-13). We perform proof-of-concept high-dimensional one-way quantum operations, where the cluster states are transformed into orthogonal, maximally entangled d-level two-partite states by means of projection measurements. Our scalable approach is based on integrated photonic chips(9,10) and optical fibre communication components, thus achieving new and deterministic functionalities.