Have you tried to graft it onto another tree or onto a seedling? That might be the most successful way to keep the tree.

I found one link regarding growing it from cutting. It says to use a 1:1 peat and sand ratio. I would recommend taking a lot of cuttings and trying all the different techniques they talk about in that link because youll have a higher chance of success that way.

Scroll a little ways down in the link i included. It is in the section named "Cuttings and Air-layering".

Here is a link that might be useful: mango propagation

You need a rootstock. You can: grow a mango from seed (which you don't have time to do) and then graft onto it, or graft a branch onto an existing mango tree (but this wouldn't give you "your" mango tree...just one branch of it, or buy a small mango tree, cut the top off, and use the scion from the tree that you have to cut down (I would do #3). I have linked two videos/pictorials on how to graft mango trees from an old post of mine:

http://forums.gardenweb.com/forums/load/tropicalfruits/msg062152499440.html

Good luck!

Just as bluepalm said. You need to graft it onto something (rootstock). A cutting does not have the same rootsystem as a plant that came from a seed. From the seed you have one main rootsystem and then a branched rootsystem comes off the main. With cuttings you have a cluster of similar roots coming from the base of the cutting.If you try rooting it, it might take, but will not survive (grow into a tree). Most tropical fruits are either produced from seed (takes longer to set fruit and might not breed true)or grafted onto rootstock produced from seed. There are only a handfull of tropical fruits that are actually sucessfully propagated by either cuttings or airlayering.
Even those that can be propagated by cuttings are most of the time grafted, since a grafted tree has a better chance of becoming a well established tree.
Just my 2 cents

I'm trying to grow a mango tree for my uncle who's selling his house that has a big, beautiful mango tree on the property. The fruit are amazing on this tree. The house closes escrow in a week, so I need to get what I need from the tree by then. This time of year, there are no fruit, no seeds..
Can I get a limb to sprout roots? Or, do I need to graft to another mango tree? If I graft, I won't know if the fit will turn out as good as the original, right?
Thank you.

May be worth trying this. Get some spagnum moss. Then select the branch you wish to propagate. Strip some bark both sides of the branch without cutting thru to the wood. Wrap the spagnum moss (now wet) firmly round the branch and cover with cling rap or similar and secure both ends. The roots should grow into the spagnum moss. When this happens cut branch and pot up. Alternativly if a branch is close to ground the selected branch can be stripped of bark and layered into a pot or ground direct. This is called layering while the first method is airlayering. It probably an old fashioned method but it works well for plants that are difficult to take cuttings from

Hope this helps.

PS you could also try some rooting hormone on the cut surfaces before wrapping with wetted spagnum moss. Also squeeze out the moss as it holds a lot of water.

look for branches as pencil thickness then cut it and make some cutting fron it measuring not more than 10cm then remove all the leaves then soak in water for sometime in water after that make a pot filled with mud,bit fertilizer and sand mixed.Then take out the cutting then apply the powder that is called rootx or cinnamon powder then plant into the pot after 3 weeks you will het the result.