Guy G just stole my advice. I would highly recommend you go with a small fixed blade instead of a folder. A folder is going to get gummed up with sap and stuff, not to mention the dirt. My wife is a horticulturist and I loaned her my Benchmade AFCK (liner lock) for a day. She used it to cut.. I want to say it was yucca rhyzomes or something like that that grows in sandy soil. When she came home, it was duller than you can believe and I had to really work to get all the dirt out of it.
My recommendation is that you get a few separate tools, as I don't think there's a single knife that would do all of the tasks you mentioned very well. For grafting you want a thin, hellishly sharp blade that doesn't need to be very long. For digging or chopping, you want a longer, thicker blade for more weight and thus momentum. For digging, you want a trowel. For dividing roots, you want something with very high abrasion resistance.
For pruning small branches, deadheading flowers, etc, get a pair of Felcos. (my wife recommends the #2's)
http://www.midcitynursery.com/shopping/felco.htm
For pruning larger branches, just call the arborist!

But if the arborist isn't available, get a japanese-style folding saw. We've got a Silky and it's AWESOME.
http://www.dustbeegone.com/foldingsaws.htm (we've got the F-180)
For grafting, they have special knives...
http://www.rittenhouse.ca/asp/Product.asp?PG=1790 or you could get something like a small Swiss Army Knife. The SAK blades can get scary sharp, and are nice and thin. Get one with two non-serrated blades, and use one for utility tasks while saving the other one for only grafting.
For dividing roots while staying fairly small, you could try a Swamp Rat Bog Dog. They've recently released some shots showing that it can take a beating, and the D2 steel is known for high abrasion resistance. Also, it's not a coated blade or anything, so it's not too terribly "tactical looking". Eric Isaacson's wife uses a Battle Rat for dividing while Voracious uses a Camp Trap. My wife agrees that the longer blades of those knives would be better if you were going to be dividing things in, say, gallon pots, but the shorter Bog Dog is probably more sheeple friendly.
http://www.swampratknifeworks.com/cgi-bin/ultimatebb.cgi?ubb=get_topic;f=10;t=001946
http://www.swamprat.com/knives.html#bogdog
I know that this is probably more than you wanted to spend, but think of it as an investment in your work. You could save some money by using the Bog Dog for grafting and general utility work, but you would have to sharpen it up just for grafting when you think you're going to do some of that. I know that the Bog Dog is bigger and scarier than a polite folder, but the optional leather sheath looks very tool-like, and once the people see you use it a few times, they'll be asking to borrow it.
Hope this helps!