People sometimes comment that their cutters are leaking. Most cutters of the pencil type are not prone to leaking. Some of the pistol shaped cutters seem to have more difficulty.
One possibility is that the oil being used is too thin for the system that dispenses the oil. In that case a little thicker oil may cure the problem.
It may be that the oil is leaking from some where else than the valve or wick that is intended to dispense the oil. This sometimes happens when excessive pressure has been put on plastic handled cutters whether pencil or pistol. In this case, the alternative is to replace the cutter or use another method.
The other method could be called the dip and cut method. In this case you leave the reservoir empty and have a shallow container filled with oil soaked cotton wool. Dip the cutter wheel into the cotton wool before each cut and this will give you enough lubrication for the score. A variation on this is to dip a brush in a container of oil or turpentine substitute and paint along the line of the cut before scoring. Both are effective.
Although it is not a repair, you can push a cotton wool lump down to the valve or wick, saturate it with oil and then there is enough oil to lubricate the cutter wheel, without an excess to leak out. You do need to renew the oil for the lump of cotton wool from time to time.