Critical properties in photoemission spectra for the one-dimensional Mott insulator with orbital degeneracy are studied by exploiting the integrable t-J model, which is a supersymmetric generalization of the SU(n) degenerate spin model. We discuss the critical properties for the holon dispersion as well as the spinon dispersions; hy applying the conformal field theory analysis to the exact finite-size energy spectrum. We study the effect of orbital-splitting on the spectra by evaluating the momentum-dependent critical exponents.