Yes and armed Mig 25 could only do about 65000ft (the recon version could do about 80000ft) and a max speed of Mach 3.2. The SR71 max ceiling was about 20000 ft more, however you put enough aircraft in front of an on coming SR71 and start lobbing missiles at it, you are bound to hit something.
the 25s were armed usually with 2 IR Acrids and 2 Radar Acrids, and doctrine when hunting SRs was to fire one of each, wait 5 secs, and fire the other 2. The Acrid with a top speed of about Mach 4.5 could easily catch an SR providing the range was there, and definitely take it out from a front on attack. These missiles were huge, slightly bigger than a US Hawk SAM missile (bigger than a Phoenix as well), and with a 70kg warhead, wouldn't have to hit an SR to take it out, merely a proximity shot would have been enough with a warhead that big.
As well, the SR handles like a dump truck, so doubtful they could maneuver enough to get away from the missiles.
The kicker was, that the SR was stealthy and fast enough that by the time the Soviets reacted and sent something up, the SR was likely already by them.