In this paper, we report the discovery of two new super Li-rich K giants: HD~24960 and TYC~1751-1713-1. Based on high resolution ($R\approx 60,000$) spectroscopy, we have derived Li abundance of A(Li)$\approx$4.0~dex for both stars. Other elemental abundances are normal of typical K giants. Low ratios of [C/N] $\leq$ $-$ 0.25 and $^{12}C/^{13}C \leq10$ suggest that the stars are in upper RGB phase. Further, based on Gaia astrometry and secondary calibrations using Kepler asteroseismic and LAMOST spectroscopic data, we argue that both stars belong to red clump (RC) phase with core He-burning. Results add to half a dozen already known red clump Li-rich K giants, and support the growing evidence that the origin of Li excess in RC giants seems to be associated with either He-flash at the tip of the red giant branch (RGB) or recent planet/ brown dwarf merger events closer to the RGB tip.