Razors should be placed in your general waste bin.
You could try a traditional safety razor instead which allows you to keep the razor and the razor head. They just require you to buy and throw away the razor blade itself.
Classic safety razors have been around for a little over a hundred years and come in a variety of different styles.
The razor itself ranges in cost from $25 to over $100, although you can find cheaply made ones for less and can sometimes find a deal on an antique razor. The blades typically only cost about $0.50 each.