We're moving into a home that has a kitchen sink which is not configured the way I'd like. I want to replace it with a dual sink. However, the sink is overmounted onto a Corian countertop. Is this a DIY project or would we have to call a professional?

What type of sink and how affixed to the countertop?

It's white porcelain and appears to be affixed with putty. We haven't investigated it thoroughly, yet, as we're just buying this house. We wanted to see if this was even possible before we start making plans to change it out.

Yes it's possible and not hard. Corian can be cut with a jigsaw or plunge router.
Then there's the width of the cabinet under it... usually only 2 - 5" wider than the sink.
And if there's a dishwasher directly next to it, then the wider sink has to go all the way to the other side.
And if it's positioned in the middle of a window...

There's an old saying about buying a house: live in it for 6 months before starting the renovations.

We don't know your skill level but I would consider this 2-3 hammers on a scale of 4. You may have to enlarge the opening or move things a bit but totally DIY possible. Silicone or bath siliconized acrylic caulk to seal. Use the flange mounted connectors.