Keep in mind, when running a CPU intensive operation in Node the whole application blocks as it runs in a single thread. If you're going to run a CPU intensive operation in Node, make sure you spawn it off into a child process who's only job is to run the calculation and then return to the primary application. This will ensure your Node app is able to continue responding to income requests as the data is being processed.
Now, onto your question. Having the database on a different server is extremely common and typically is a good practice to have. Where you can run into performance problems is if your database is in a different data center entirely. The further (physically) your database server is from your application server, the more latency there will be per request.
If these requests are seriously CPU intensive, you should consider looking into a queueing mechanism for a couple reasons. One, it ensures that even in the event of an application crash, you don't lose a request that is being processed. Two, you can monitor the queue, and scale the number of workers processing the queue in the event that the operations are piling to the point that a single application can't finish processing one before another comes in.