J2EE web applications
must not terminate threads. If it doesn't say that explicitly in the spec, you can consider it said implicitly in that the spec expressly and explicitly forbids creating threads.
The threads used to service an HTTP service request belong to Tomcat, not to the application. Requests should be processed and completed, which returns the thread to the Tomcat thread pool. If you terminate the thread instead of returning it, your server's life will be short, brutish and nasty.
An inherent assumption - or perhaps requirement - for HTTP request processing is that the request/response cycle should be as short as possible so that A) response will be returned to the user/client with minimal delay, and that B) common resources, such as the Tomcat processor threads, should not be tied up and thus unavailable for other users. If you need to do work that cannot conform to these constraints,
you should construct an out-of-band processing engine for that kind of work. This engine is typically started via a ContextListener at webapp startup, and usually has an associated work queue so that it may spawn whatever threads it needs independently of the HTTP request/response processor threads. HTTP requests may queue up work and hand it off to the engine, but they may not call the long-running engine code directly (otherwise, what's the purpose?)
The engine thread(s) may spawn cancellable threads, but forcible termination of a thread is never a good idea, which is why the primary methods originally in Java were deprecated. If the reason for wanting to terminate a thread has to do with getting hung on a request to an external network-based service - including database requests - the preferred method of termination is to adjust the timeout parameter for that service (if there is one). For long-running processes in local code, it's safest to have the process check periodically for a "cancel" flag that can be set by the requester so that the process will be able to short-circuit its normal work and clean itself up in an orderly manner.