Massive formaldehyde emissions have seriously endangered environment and human health, while predictably polymer aerogel is a promising candidate for formaldehyde (FA) removal, whereas low FA adsorption capacity, high volume shrinkage, and mechanical brittleness restrict its further development. Herein, based on “rigid-soft combination” polycondensation strategy, trifunctional 1,3,5-benzenetricarboxaldehyde (BTC) and polyetheramine Jeffamine T403 are selected as building blocks to construct a novel amine-linked polymer aerogel (rBTA) with hierarchical micro-nano porous structure via mild sol-gel method and freeze-drying process. Stable amine linkages in rBTA are formed by NaBH4 reduction of imine bonds, improving acid/alkali resistance and chemical stability greatly, and creating numerous active amine sites for reaction with FA. Formation of robust 3D covalent network facilitates to simultaneously achieve ultra-low-shrinkage (5.4%), high specific compressive modulus (5.32 kN·m·kg-1), remarkable mechanical durability/fatigue-resistance, flexibility, and machinability. Benefiting from synergistic physical-chemical adsorption effect, FA adsorption capacity and removal ratio of rBTA reach as high as 459.84 mg·g-1 and 97.87%, respectively. Colorless rBTA is further ground into powders for preparing polyoxymethylene (POM)/rBTA composite without affecting its color and formaldehyde emission amount at 60/230°C effectively decreases by 66.87%/79.55%. Furthermore, rBTA exhibits hydrophobicity, low thermal conductivity, and high solar reflectance, being successfully applied in emulsion separation, thermal insulation, and energy-efficient buildings fields.