Have you ever had your website go down due to an attack? or if not go down slow down completley? It hapens all the time - most webhosts the people who manage the computers on which your website and email revise generally guarantee that your services will have a 99% uptime - sounds impressive doesn't it? until you do the math and realise that 1% is about 3 and a half days worth of downtime per year!
Most people I talk to seem to think that if you wish to run your email on a seperate server that perhaps has no website on it and thus is less prone to attck then you would need a differrent domain name for your email as opposed to the website address so instead for example of your email ending @deemo.co.uk for example it would have to be @deemo-email.co.uk.
This however is not the case at all, a few changes in something called the DNS can see your email diverted through an entirely differrent server - we currently recomend our clients consider Zoho Mail for this sort of service - they offer business level email with a free starter package and the promise 99.99% uptime which equates to less than an hour downtime a year! a vast improvement I'm sure you would agree. The service also offers you far more sophisticated control over your email than you would get from a standard webserver package.
If your one of our clients and you would like to discuss this further we can certainly help you with the setup just give us a shout.