The integration of thermal/fast neutron spectroscopy with gamma-ray detection in a single compact system remains a major challenge in radiation monitoring. Here, we present a novel dual-mode detector design based on isotopically enriched Cs \(_2\) LiYCl \(_6\) :Ce (CLYC) crystals coupled to high-gain silicon photomultipliers (SiPMs). By utilizing the distinct scintillation decay characteristics of CLYC for neutrons and gamma rays, we achieved excellent particle identification performance through an optimized charge-comparison pulse shape discrimination (PSD) algorithm. The \(^6\) Li-enriched CLYC-6 enables efficient thermal neutron detection via the \(^6\) Li(n, \(\alpha \) ) \(^3\) H reaction, while the \(^7\) Li-enriched CLYC-7 exploits the \(^{35}\) Cl(n, p) \(^{35}\) S and \(^{35}\) Cl(n, \(\alpha \) ) \(^{32}\) P reactions for fast neutron spectroscopy. Our CLYC-6 (95% \(^6\) Li) thermal neutron-gamma detector exhibits a gamma energy resolution of 6.52% at 662 keV, with a figure of merit (FOM) value reaching \(\sim \) 3.84 for thermal neutrons. The CLYC-7 (over 99% \(^7\) Li) fast neutron-gamma detector exhibits a gamma energy resolution of 6.73% at 662 keV, with an FOM value reaching \(\sim \) 2.35 for fast neutrons; moreover, there is a good linear relationship between the fast neutron energy and the corresponding peak position in the energy spectrum. The quenching factors for protons and \(\alpha \) particles are calculated to be 0.90 and 0.53, respectively, for the reactions \(^{35}\) Cl(n, p) \(^{35}\) S and \(^{35}\) Cl(n, \(\alpha \) ) \(^{32}\) P. Our measurements demonstrate that the SiPM-based readout not only supports significant miniaturization but also preserves the excellent intrinsic spectral performance of CLYC. This work lays a solid experimental foundation for next-generation portable, magnetic-field-insensitive multi-mode radiation spectrometers.