1) A skein of yarn according to Halliwell; properly 120 rounds of the legal reel and 91 inches long (OED). It is apparently a northern word.
1624 Two women for stealing thirty cuttes of linen yarn, Thirsk
1637 3 scoore cutes of garne, 4s, Selby
1726 notice to all persons that expose to sell in the said market any linen yarne, that the same be ... full tale of six score threeds to the cut upon a reele, Guisborough.
2) A passage or channel; an artificial watercourse.
The word occurs in early place-names: c.1235 tres perticatas in Cutthesik, Whitwood. From the late eighteenth century it came to be the colloquial word for a canal but in earlier contexts had to do mostly with the realignment of rivers. It occurs as a verb at an early date: 1649 to Cutt the said banck, sandbed or stayner thorough and demolish it, Horbury. When bridges collapsed it was often because the even flow of water through the arches had been disturbed and the foundations of pillars and abutments weakened. The records show that attempts were frequently made to stop this happening by changing the course of the water and there is explicit information in a document relating to Bishopton Bridge. In 1754, the usual course of the River Laver had been diverted by frequent floods and the rapidity of the rivulet, and a report at the Quarter Sessions contained the following information about the need for a cut:The rivulet … will in a short time wash away the High Road leading from Pateley Bridge through Bishopton Ellers towards Ripon [and] the large beds of gravell and stone that are thrown up … will obstruct the same in its course … and the river will get behind the wall built for the security of the bridge … unless a proper cut be made thro’ the said beds of gravel and stone to carry the said river thro’ the said bridge.Previously, in 1683, a great Trench or Cutt was made to bring the River Ure more directly to Hewick Bridge and similarly it was agreed in 1712 to bring the River [Aire] into a straight course by making two Cutts thorow the grounds of a local estate. Alternative words used were trench and ditch, and in 1681 work on Rotherham Bridge entailed the digging of a ditch which took a large labour force the best part of June and July.