There are certainly hunters probably better qualified to answer this question, but I will take a stab at it. With elk there is some breeding activity the last few days in August and the first 10 days or so in September, but if by rutting you mean the peak of bugling (so you can find bulls easier) I would have to say the last 10 days of September and the first 4-6 days of October. Therefore the end of muzzleloading season or the last week of bow season usually correlates well to some bugling/rutting activity.

As far as Mule deer: There rut normally starts in Mid November and runs into the first week or so of December. This is after most hunting seasons have closed, but in some areas, they are offering a 4th rifle season which should correlate better to the mule deer rut.

Where are you going to hunt in southwest Colorado?