Copper line to fridge

If you have a saddle valve clamp that is closed yet still letting water through, you may simply have to turn the handle a bit more with force to drive the pin tighter to the copper pipe.

HOWEVER: If it instead breaks you have a bigger problem to solve.

If you only wish to temporarily block water in a copper tube, squashing it flat with a tight vice grip pliers can work until a replacement saddle clamp (or better a genuine T fitting with valve) is installed. A leaking copper tube can easily be spliced unless corrosion was the cause. There are many variables and I don't have enough info from you to know exactly what is happening and what your ultimate goal is..

Take some cell phone photos to post of the leak and of the valve. Or bring those to the hardware store (but confirm the skill of the clerk before you listen!). All the needed parts are easily purchased. It can be fixed by anyone comfortable with a screwdriver and adjustable wrench.