I've walked right by the takeoff to Guthrie Mountain many times on my trips along the Green Mountain trail. I've always thought "I'll do that next time". I should have done it sooner, because this turns out to be a fun little-known peak to bag in the Catalinas. Sitting at roughly 7281 feet, Guthrie does not see a lot of visitors though it is surely worthy. There is even a nice little trail that runs out to it's summit. This hike can be started from either end of the Green Mountain trail; the lower General Hitchcock campground or the upper Green Mountain trailhead at milepost 18. This description will be from the upper trailhead since it is higher in elevation and slightly cooler this time of year.
The Green Mountain trail is fully described on this website and I reference you to that description for details. Briefly, the Green Mountain trail takes off from the Catalina Highway and runs mostly east and south, offering different views of the Catalinas that what most are used to. It descends nearly the whole way too, so you gotta climb on the way back. There are areas along the way that were burned in the fires and the recovery process is underway. The trail is always easy to follow. Along the way there will be two signed takeoff points for the Brush Corrals trail, at roughly 0.2 miles and 1.2 miles from the trailhead. Just follow the route of Green Mountain. There are frequent views north and east, which tend to be very long.
Just past the signed takeoff for Maverick Spring, you will reach a nice saddle with a sign pointing the way to the General Hitchcock campground. This is Bear Saddle and you will know when you are here. To the left is Guthrie Mountain and there is actually a little tin homemade sign nailed to a tree indicating the use path to it's peak. This is roughly 2 miles from the upper Green Mountain trailhead.
Jump on the path to Guthrie Mountain. It is actually pretty easy to follow, I was surprised at this. There are cairns present too, though they are not really necessary. There is a lot of interesting red rock on Guthrie, I'm not sure why. The route to the peak is about 1 mile in total. The path climbs to the ridge and runs it for a while offering you views of your goal. It then descends down a small saddle before climbing back up to the summit proper. It's a decent little climb. The last part of the climb before the top is a little exposed up some slick red-colored rock. It's a very short segment though, then up to the forested summit. If you scramble around you can climb up some boulders and get outstanding views of the eastern Catalinas, as well as north. Not the typical stuff I'm used to seeing up here. Worth it just for that.
To get back just retrace your steps and remember that there is some good climbing to do on the way back.