Canyons are inherently risky. Flash floods occur without notice on sunny days. Technical skills & surrounding topography knowledge required yet does not eliminate risk.
Take a step back in time
Sawmill Canyon is best described as a non-technical canyoneering route. There is only a trail from the parking lot to the river, after that you cross the river you follow the canyon upstream as far you like. Swimming is required if you want to fully enjoy this canyon, so plan accordingly. Also make sure you pick up a San Carlos Indian Reservation recreational permit before you start hiking.
Pick up the faint trail from the parking area towards the old trail switch backing down towards the Salt River. The trail cuts out just above the river, so find the best line down to the river. Before wading/swimming across the river, look upstream a bit and locate the canyon that drains in the river. As you swim across aim for the rocks that jut out just upstream from the canyon. Otherwise you'll do like me and exit the river at the muddy bank and sink in 6 inches with every step.
As you ascend the canyon you'll be trying to avoid the vegetation most of the way. I managed by following a faint canyoneer trail or sticking to the watercourse whenever possible. When I first entered the canyon, I noticed that it wasn't flowing and the first few pools were stagnant and murky, but don't let that detour you from venturing further up. You'll soon hit a series of (dry) falls on the left and a taller one on the right. You avoid these by climbing the rocks in the middle. There's a large pool on the left side below the upper falls that I recommend swimming and diving into. When it's not flowing, you can also climb up the falls at the end of the pool. Soon after the falls, you'll hit a narrows section that you want to avoid by climbing the rocks on the left. The narrows are very slippery and smooth and the pools are mossy and murky. Not to mention that at the end of the narrows are some large choke stones that prevent you from climbing out.
After avoiding these two main obstacles, the rest of the canyon is fairly straightforward. I'd recommend going about 2 miles up canyon before turning back. At this point the canyon starts to open up and isn't quite as scenic. But up until this point you'll see impressive cliffs lining the canyon, many caves imbedded in the walls, large pools of water filled with underwater plants, and many dried up pools leaving a white residue on the creek boulders. When I came thru there were 2 mandatory and 3 optional swimmers that I thoroughly enjoyed. At first, wading thru the water plants was kind of eerie, but you get used to it after a few times. The last pool was very deep and took you thru this long hallway that ended just before the canyon opened up. This is a great place to have lunch and soak the canyon in. Enjoy!
WARNING! Hiking and outdoor related sports can be dangerous. Be responsible and prepare for the trip. Study the area you are entering and plan accordingly. Dress for the current and unexpected weather changes. Take plenty of water. Never go alone. Make an itinerary with your plan(s), route(s), destination(s) and expected return time. Give your itinerary to trusted family and/or friends.