Finally, we get to do something with the actual sword rather than worry about hurting ourselves and others. Does that mean we are all in the clear? Of course not!
Check, recheck and keep a constant eye on your surroundings
I can't emphasize this enough. If you do something stupid and hurt yourself it is one thing, but if you inadvertently cause harm to someone else it is another. (Though anyone hurting themselves while cutting casts a black mark against training with sharp swords in general, so don't think I don't care about your safety as well. :) )
Always maintain your balance and grip on the weapon
If you are cutting in a balanced stance with a proper grip on the sword there are only a few things that can go wrong. If you are off balance, or lose control of the sword all bets are off.
Do not cut towards the lead leg
Of the few things that can go wrong if you cut in a balanced position, cutting into your lead leg is one of them. Make sure you cut away from your lead leg.
<Lead leg picture>
Make sure you have good footing
Obviously you should never be cutting if you have a chance of slipping. Keep track of the ground condition over the course of your cutting session. After going through a few targets the debris can start to accumulate and present a tripping hazard. Keep the cutting area clean! Also remember that most cutting targets involve water, and as the ground gets wet it can get slippery.
Keep your hands clean
Hands can get wet from handling cutting medium and make it harder to grip the sword. It can also be a problem if oil from the last blade cleaning is left on the hilt, so make sure the sword has a good grip as well.
Mount the target properly
Given enough time spent cutting you will fail to cut the target and/or miss and hit the stand. Make sure that the stand you are using is appropriate and will not cause a dangerous reaction (such as collapsing unpredictably while you have a sharp sword in motion.)
Do what you know
Test cutting is meant for you to test the skills you have practised in regular drilling. Introducing new cuts or footwork patterns is best left for appropriate simulators and not with live blades!