I bawled like a baby throughout my daughter's "lasts" in high school. The funny thing is, that actually made it easier for me when it came time to say good-bye. I had gotten a good deal of my grieving for the end of this phase of my life out and over with. After we said goodbye, the house seemed emptier, but I adjusted and went forward. Most parents do. (By the way, I find that I am doing the same with my son (who thinks I am a little unhinged right now) as his high school days wind down).
If your mother truly is going into a major depression, then by all means suggest she talk to a professional. But, sometimes sadness is part of the process of saying good-bye and watching our kids start their lives. It is, after all, a turning point for everyone in the family. Letting your mother know that she's still important and will still be part of your life helps. Hugs help too.
Also, think of some ways you can let your mom know that you'll still be in her life. One of the nicest gifts my daugther ever gave me is two weeks before she left for college she put me in the car and drove up to a special spot we'd visited before in the mountains. She had packed drinks and snacks, and we sat there and watched the sun go down together, just enjoying each other's presence. Another nice thing she did for me and my husband was to hide all sorts of little "love notes" throughout our house before she left. Each one felt like a hug, and it took us months to find them all. Great minds think alike, because before we left her in her dorm room, I'd tucked my own share of "love notes" here and there for her to discover.