The answer to that is yes you can. A lot of people tend to get hot and cold water mixer faucets because there will be a wider range of designs to choose from and the designs are usually better than the single output faucet. 

So when fixing your mixer faucet to just a single input, you would need to get a Y joint to complete the connections. As illustrated in the photo below, simply connect the input source of the water to the Y joint (as indicated by the blue arrow) and connect the pipes from the two outputs of the joint to your faucet (as indicated by the green arrows). Now you will get a constant flow of water no matter which direction you turn on your faucet from.