You need to set your Tomcat classpath properly. The files aren't really compiled with the mysql.jar (unless you're using MySQL specific classes in your code which is often unlikely), so the file is rarely not used during compiling.
It is, on the other hand, used directly at runtime. You may need to place the jar into the WEB-INF/lib directory of the web application. It's been awhile since I've used tomcat, so I could be off on that. Other than that, try updating the classpath for tomcat to find the jar you placed.