Racing spec tyres with softer compound often cut.
Regular checks and flint removal is important.
Repairing the cuts is easy and worth doing to avoid stuff getting in the cut and giving you many many punctures.
Your Blue Peter cut out and keep guide:
1) Take tyre off wheel.
2) Remove all flints, glass etc.
3) Find 1st cut of notable size.
4) Squeeze tyre to open up the cut.
5) Drop in a small blob of super glue.
6) Squeeze cut closed and hold. Best to wipe away excess glue with wet cloth now. Also helps to fold tyre in on the cut to really force it closed tight while the glue starts to set. Hold for about a minute.
7) Move on to next cut and repeat process.
Leave tyre for 24 hours (or at least overnight) before re-fitting to allow the glue to fully harden. If you re-fit and inflate back up to 100psi straight away the glue hasn't set enough and it can open the cuts up a bit.
I do this whenever I notice a larger/deeper cut (even down as deep as the casing so long as it hasn't gone all the way through). Never had a problem with a "repaired" tyre like this, the cuts are never that big or they'd have caused the tyre to fail and the tube to blow out otherwise.