After several years of playing with various deltas, homemade nasa kites and my favorite an Ozone LD Stunt I bought a Ozone Cult 3.5m. It's great but I don't get what the line joining the two handles together are for. I find them a nusance and I am tempted to cut it off. What the purpose of this line?

Sounds like a strop. It is to hook into a latch on the front of a harness. Without the harness, it would make it hard to settle line twists and tangles and of no benefit to you at all.

Yup, it's a link line or strop. You can take it off of your handles without cutting it. Both ends are attached by a larks head. Just undo one of the ends and pass the handle all the way through through the loop to get it off. The other end will come off much easier once the first one is disconnected. Save the link line for the time that you ever do get a harness.

Ok, that came off fairly easily. Thanks guys, that's better than cutting it off.
I've never used a harness but I have used (with other smaller kites) a webbing strap from the handles around my back to take some of the load off my arms, which worked well. This is probably not safe for the bigger Cult as it would prevent the kite killers from working. If the strop line was hooked onto a harness would the load on the lines not force the handles together? Is is easy to unhook from a harness?

It depends on the style of harness. Usually the harness has a simple metal hook attached that allows you to hook the link line in and out very simply. Other systems latch into the harness and will need a safety release system to disconnect from. Whatever system you have just make sure that you can unhook from it under extreme loads immediately and with very little effort.