It is challenging and vital to develop coordination polymers (CPs) with an outstanding sensing performance. In this work, CP-based sensors with active S and N sites are first exploited. Three new Cu-CPs [Cu(L)(SCN)2·2DMF]n (1), [Cu(L)(SCN)·2DMF]n (2), and [Cu(L)(CN)·2DMF]n (3) were successfully synthesized by 9,10-bis(di(pyrimidin-5-yl)methylene)-9,10-dihydroanthracene (L) and SCN-/CN- ligands. 1 demonstrates a 1D wavelike chain, fabricated by L bridges linking with Cu(SCN)2 units. 2 exhibits a 2D (3,3)-connected network fabricated by SCN-, 3-connected L, and Cu units. 3 exhibits a 3D framework, built by 4-connected Cu centers, CN-, and L bridges. 1-3 have good water, pH, and thermal stabilities. 1 and 2 have uncoordinated S and N active sites and can detect Hg2+ through the fluorescence enhancing ("turn-on") effect. Meanwhile, 3 only has uncoordinated N active sites and shows a negative Hg2+ sensing ability. 1 and 2 have ultrahigh Hg2+ sensing sensitivity and selectivity. The KSV and LOD of 1 toward Hg2+ are about 3 and 5 times superior to those of 2, separately. 1 and 2 represent the first S- and N-rich CP-based sensors and exhibit an excellent "turn-on" Hg2+ sensing capacity. Their "turn-on" Hg2+ sensing mechanism and difference sensing performances are discussed in detail.