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This work demonstrates the spectrum-clean shear-horizontal surface acoustic wave (SH-SAW) resonators with large electromechanical coupling coefficient ( ${k}_{\text {eff}}^{{2}}{)}$ and substantial admittance ratio ( ${A}_{R}{)}$ in a lithium niobate on insulator (LNOI) platform in the gigahertz range. The solidly mounted LN waveguide is acoustically engineered through optimal selection of wavelength ( $\boldsymbol {\lambda }$ ) and electrode thickness for eliminating the undesired Rayleigh SAW mode while enhancing the ${k}_{\text {eff}}^{{2}}$ of the SH-SAW. Consequently, the transverse spurious modes are suppressed using repetitive cross-interdigital transducers (X-IDT), with minimal tradeoffs to other key performance parameters. As a proof-of-concept, the SH-SAW resonators are fabricated on a 1.2-/0.5-/500- $\boldsymbol {\mu }\text{m}$ YX-LN/SiO2/Si functional substrate with gold electrodes, exhibiting a resonant frequency of 1.17 GHz, a ${k}_{\text {eff}}^{{2}}$ of 43.3%, an ${A}_{R}$ of 74.3 dB, and a spectrum-clean response at $\boldsymbol {\lambda }$ of $2.6~ \boldsymbol {\mu }\text{m}$ with only a few minor spurious modes away from the main mode, offering significant potential for applications in wideband RF circuits.