I've done some digging and it appears that Arizona has experienced a lot of significant tornadoes for a western state. I'll list some examples going back to the 1920s. There might have been strong tornadoes before then that I'm not aware of.
9/14/2011 Humpherys Peak EF2
This short-tracked high-elevation tornado produced significant forest damage at elevations of over 10,000 ft.
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10/14/2006 Camp Navajo F2
Despite being listed as an F1 in Storm Data, the local NWS gave this tornado a low-end F2 rating as it snapped off large pine trees near ground level.
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10/18/2005 Dinnebito Wash F0
Despite only being given an F0 rating, this tornado was probably stronger at some point as it tracked 30 miles over barren desert. Several outbuildings were destroyed or carried over 100 yards, a filled 55-gallon drum was found empty hundreds of meters away from its original location and there was considerable damage to trees.
10/24/1992 Sunset Crater F2
Around 700 ponderosa pine trees were snapped or uprooted by this 200-yard wide tornado. 260 acres of timber was destroyed.
7/22/1984 Santan Mountain F1
This "large and intense" tornado formed in the Giles Indian Reservation. Due to it occurring in a rural area, no structures were damaged besides some power-lines. 25 wooden power poles were ripped off 4-ft above the ground. The tornado was estimated to be 1500 yards wide.
6/23/1974 Tucson F2
This deadly tornado killed one person as it tore through a mobile home park. Multiple mobile homes disintegrated.
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8/30/1971 Tempe F2
This strong tornado injured 41 people as it tore apart mobile homes, unroofed frame homes, and downed power-lines in the town of Tempe.
TornadoTalk Article
8/27/1964 San Xavier F2
This killer rope tornado resulted in one fatality as it hit the San Xavier Mission area. Homes were destroyed and an adobe covenant was severely damaged.
TornadoTalk Article
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4/8/1926 Phoneix F2
This brief cone-shaped tornado destroyed six small homes at the eastern edge of Phoneix.