That special tapered punch is known as a drift. It's wedge shaped and is driven into a slot in the spindle to force the drill chuck's MT2 tapered spindle out.
While I've never seen a draw bar on something with a spindle as small as one like yours, on most mills, the collets go in the bottom of the spindle and are drawn up by a long threaded bar that sticks out of the top od the spindle when in it's full up position. Make sure your machine doesn't have a draw bar before using a drift. If it does, then the procedure is to back the draw bar out a couple turns and whack it with a brass hammer lightly until the chuck or collet come loose.
Holding an endmill cutter in a drill chuck will only allow you to take very light cuts and you can probably expect poor accuracy as the chucks are not going to hold the cutter with any appreciable concentricity. As mentioned above, a couple MT2 end mill holders would be a lot better choice. HF lists a 1/2 and a 3/8 MT2 endmill holder for around $10.00 ea.
Having said that, you will grow to hate using a mill with an MT2 taper unless you use cutters with teh same size shaft all the time because it's a royal pain to change the endmill holders. If I were in your shoes and could swing it, I'd return that thing and spend a few more dollars for this model:
http://www.harborfreight.com/cpi/ctaf/Displayitem.taf?itemnumber=44991
It has a WAY more standard R8 taper spindle just like a real Bridgeport with a draw bar meaning it's a 30 second operation to change a collet and there are a HUGE number of things available to fit an R8 spindle. The machine is still very light weight but would be a lot more useful in my opinion.
Something like this would take you a lot closer to a real milling machine:
http://www.harborfreight.com/cpi/ctaf/Displayitem.taf?itemnumber=33686
I have seen them go on sale for $599.00. It's WAY more rigid than the minis, but at 700lbs is also a lot more difficult to deal with if you're in a small shop working by yourself. It really doesn't take up much more room than the mini, but does cost more and is harder to move. This mill/drill is sold under a lot of different names and is made by Rong Fu. It's real name is an RF31 and these things show up all the time used for around $500.00 and usually with a bunch of extra tooling. Just some things to think about.