Heteroatom-rich porous-organic-polymers (POPs) comprising highly cross-linked robust skeletons with high physical and thermal stability, high surface area, and tunable pore size distribution have garnered significant research interest owing to their versatile functionalities in a wide range of applications. Here, we report a newly developed organogel-assisted porous-organic-polymer (POP) supported Cu catalyst (Cu@TpRb-POP). The organogel was synthesized via a temperature induced gelation strategy, employing Schiff-base coupling between 2,4,6-triformylphloroglucinol aldehyde (Tp) and pararosaniline base (Rb). The gel is subsequently transformed to hierarchical porous organic structures without the use of any additive, thereby offering advantageous features including extremely low density, high surface area, a highly cross-linked framework, and a heteroatom-enriched backbone of the polymer. During the semi-hydrogenation of terminal and internal alkynes, the Cu@TpRb-POP-B catalyst with Cu embedded in the TpRb-POP structure consistently demonstrated improved selectivity towards alkenes compared to Cu@TpRb-POP-A, which contains Cu NPs exposed at the exterior surfaces of the POP support. Additionally, Cu@TpRb-POP-B showed higher stability and reusability than Cu@TpRb-POP-A. The superior performance of the Cu@TpRb-POP-B catalyst is attributed to the steric hindrance effect, which controls the product selectivity, as well as the synergistic interaction between the heteroatom-rich POP framework and the embedded Cu NPs. Both the effects are corroborated by experimental characterization of the catalysts and density functional theory (DFT) calculations.