Controlling spin interactions in magnetic-molecules/metal is essential for spintronic applications. Recent studies showed that using small molecule coordination, one could switch off the spin interactions between magnetic-molecules and metal substrates. However, this control should not be limited to the two-state switching. The strength of spin interaction can be reduced, but not "off" by the proper selection of small molecules. To demonstrate this, we considered two contrasting systems, NH3 and NO2 coordinated to Co-porphyrin/Au(111). In our scanning tunneling microscopy and spectroscopy (STM and STS), Kondo resonance was preserved with weakened spin coupling after NH3 coordination. However, it disappeared after NO2 coordination, implying "off" spin coupling. These observations are explained with our density functional theory calculation results. This study shows that small molecule coordination to magnetic-molecules/metal is a powerful way to control spin interactions at the single-molecule level.