How can I repair a tyre with a deep cut? I have some foldable racing tyres, still with plenty of tread but with some small cuts through the tread &amp; cloth.  Can I do anything to them or are they destined for the bin?
You should be able to patch the tire with a tire boot, which you should be able to pick up at your LBS. It's basically a rubber patch that you apply to the inside of the tire, where a gash is. Similar to a tube patch, but thicker. There's all sorts of things that people use for makeshift boots, too, such as a $1 bill. The important thing with a boot is that it prevents the tube from herniating through the gash.

Park Tools Emergency Tire Boot