From the Iris Dewhirst parking area (there's a water fountain right by the trailhead) follow the trail ENE into Pima Canyon. Please try to stay on the trail, as the first 3/4 mile or so crosses private property. Soon after you leave this section you enter Pima Canyon, which occasionally has a stream flowing through it. You cross this wash/stream several times and it's never difficult to get across - even when the water's flowing.
After about two miles you will see the Cleaver rising above you to the north. There is no trail that leads to the peak - you simply leave the Pima Canyon trail and start bushwhacking towards it. No one route seems to be much better than the others; however the main drainage (running south from the Cleaver) seems to be the home of many sharp plants.
Head toward the northeast end of the Cleaver itself. This is the saddle between Bighorn Mountain and the Cleaver, where the vertical northeast face descends from the summit and ends in a small hill of talus and boulders.
From the saddle, it is necessary to surmont the pile of loose talus and scree to reach the actual northeast face. From here, only fifty feet or so separate the saddle from the summit of the Cleaver, but the face is vertical and the rock less than trustworthy. There are a number of lines on this face, the easiest low 5th class (5.0-5.2). Pick the best line you can find and follow it up to the summit. Beware of loose rock.
The northeast face can be soloed; however it is safer to bring a light rack and a partner. Due to the crumbly nature of the rock, large chocks and hexes work best here. One 50-meter rope is sufficient for rappelling the northeast face, or you can simply walk down the 2nd (with a few 3rd class sections) class route off the western slopes of the Cleaver. Also, due to the nature of this hike, long, thick pants are a necessity!
If you have information about this route that doesn't pertain to any of the other sections, please add it here.