A quantum spin liquid (QSL) is an exotic state of matter characterized by quantum entanglement and the absence of any broken symmetry. A longstanding open problem, which is key for fundamental understanding the mysterious QSL states, is how the quantum fluctuations respond to randomness due to quenched disorder. Transition metal dichalcogenide 1T-TaS2 is a candidate material that hosts a QSL ground state with spin-1/2 on the two-dimensional perfect triangular lattice. Here, we performed systematic studies of low-temperature heat capacity and thermal conductivity on pure, Se-substituted, and electron-irradiated crystals of 1T-TaS2, where the substitution of S by Se induces weak disorder and electron irradiation induces strong quenched disorder. In pure 1T-TaS2, the linear temperature term of the heat capacity γ T and the finite residual linear term of the thermal conductivity in the zero-temperature limit κ0/T ≡ κ/T (T → 0) are clearly resolved, consistent with the presence of gapless spinons with a Fermi surface. Moreover, while the strong magnetic field slightly enhances κ0/T , it strongly suppresses γ . These unusual contrasting responses to magnetic field imply the coexistence of two types of gapless excitations with itinerant and localized characters. Introduction of additional weak random exchange disorder in 1T-Ta(S1−xSex )2 leads to vanishing of κ0/T , indicating that the itinerant gapless excitations are sensitive to the disorder. On the other hand, in both pure and Se-substituted systems, the magnetic contribution of the heat capacity obeys a universal scaling relation, which is consistent with a theory that assumes the presence of localized orphan spins forming random singlets. These results appear to capture an essential feature of the QSL state of 1T-TaS2; localized orphan spins induced by disorder form random valence bonds and are surrounded by a QSL phase with spinon Fermi surface. Electron irradiation in pure 1T-TaS2 largely enhances γ and changes the scaling function dramatically, suggesting a possible new state of spin liquid.