What happened is that the Anasazi deforested the area around their settlements until they were having to go further and further away for their fuel and their construction timber. At the end they were getting their logs from the tops of mountains up to 75 miles away and about 4,000 feet above the Anasazi settlements. These logs had to be dragged back by people with no transport or pack animals. So deforestation spread. That was the one environmental problem.
The other environmental problem was the cutting of arroyos. When water flow is channelled, for example in irrigation ditches, then large flows such as the run off in desert rains dig a trench within the channel. This trench digs deeper and deeper with time, and today we can see examples of arroyos up to 30 feet deep. If the water level drops down in the arroyos today then that's not a problem for farmers, because we've got pumps. But the Anasazi did not have pumps, and so when the irrigation ditches became incised by arroyo cutting and when the water level in the ditches dropped down below the field levels, they could no longer do irrigation agriculture.
For a while the Anasazi got away with these inadvertent environmental impacts. There were droughts around 1040 and droughts around 1090, but at both times the Anasazi hadn't yet filled up the landscape, so they could move to other parts of the landscape not yet exploited. And the population continued to grow.