"Mormon Ties" are a folk name for hand-hewn log ties. During the construction of the D&RG and the original D&RGW in the 1870s and 80s, Mormon contracting companies provided ties, some sourced in Utah and some groups traveling to Colorado to cut. It became one of the largest industries in the territory after farming and mining.
There's no proof that all hand-hewn ties were cut by Mormons, and they built steam-powered sawmills very quickly anyway, but it's just what people in on the Western slope of the Rockies call them.