We report on the magnetic excitation spectrum of the coupled-spin tetrahedral system Cu2Te2O5Cl2 using Raman scattering on single crystals. The transition to an ordered state at T-N(Cl)=18.2 K evidenced from thermodynamic data leads to the evolution of distinct low-energy magnetic excitations superimposed by a broad maximum. These modes are ascribed to magnons with different degree of localization and a two-magnon continuum. Two of the modes develop a substantial energy shift with decreasing temperature similar to the order parameter of other Neel ordered systems. The other two modes show only a negligible temperature dependence and dissolve above the ordering temperature in a continuum of excitations at finite energies. These observations point to a delicate interplay of magnetic intertetrahedra and intratetrahedra degrees of freedoms as expected for a system in the proximity to quantum criticality.