We report high-field magnetization, electron spin resonance (ESR), and Raman scattering measurements of the coupled spin-tetrahedra system Cu4Te5O12C14 with magnetic ordering at T-N = 13.6 K. We find thermodynamic and spectroscopic signatures for the concomitant occurrence of localized and collective magnetism. Magnetization measurements up to 60 T exhibit a spin-flop transition at mu H-0(SF) = 16 T only for H vertical bar vertical bar c as well as periodic magnetization steps at, mu H-0 = 16.5, 24.8, 33.8, 42.3, and 49.7 T, which are independent of the crystallographic orientations. For T > T-N, the temperature dependence of ESR linewidth is described by a critical power law, Delta B-pp(T) alpha (T > T-N)(-0.56+/-0.02). For T < T-N, an antiferromagnetic resonance mode is observed for 1111c, and its linewidth is given by Delta B-pp(T) alpha T3.13+/-0.04, being close to T-4 expected for a classical magnet. Raman spectra show three one-magnon-like excitations superimposed on a broad two-magnon continuum. While the two higher frequency modes show an intensity variation in accordance to a three-dimensional Heisenberg antiferromagnet, the lower frequency mode clearly deviates. These results suggest that Cu4Te5O12C14 is a unique material which shows a dual character of zero-dimensional, localized and three-dimensional, collective magnetic behaviors.