Just use the tool...

Take the upper arm off also.
Good luck getting a new cone in there with upper arm in place 

I'm guessing by your Av that your MINI is newer than 76......the spring will have course metric threads and should be fine.  Just dab some grease on the compression tool's threads to help it out.

No need to cut your trumpets....if you're installing adjustables, someone will always want your old ones......or use them in a piece of yard art.

edit:...ok, just noticed " installing spring shock "...I assume that is same as coil over....so no rubber spring needed(?)....still, take the top arm out and you can check it for wear etc.

I used the sawzal on the trumpets and still had to take the upper arm out because I was trying to reuse the cones.  The diameter of the cone was such that it interfered with the subframe walls and wouldn't come out at the angle required with the upper arm in place (it was just a hair too big).  It would only come down straight.  However, if you are going to be throwing away your cones then you could probably chop a section off of the cones to get them out.  Althought the trumpets are easy to cut, the cone metal might be very awkward, so be very careful you don't slip and damage other stuff, or yourself. 

If you use a sawzal as jwakil recommended to cut the trumpets first, you don't need to take the upper arm out. The sawzal method is the best and it took about 30 min for me to take the trumpets out with upper arm still in place.

You're supposed to be able to take it out but I found out as you did that it's very hard.  The cone is most likely frozen to the trumpet, and together they are almost impossible to take out.  I ended up taking the upper control arm out.  This was after I had cut the trumpet into pieces and was just trying to get the cone out.  (It was a good thing since I found out the shaft in the upper arm was frozen and needed attention anyway).  Since your car is newer, you might not have to go through all the stuff I did.  It took me a good week or two.  Hopefully you are installing the adjustable trumpets and won't have to worry about this in the future. 

Well rite now my biggest problem is getting the trumpet out.... it's  vary hard to get out...

Do i need to take the upper control arm off to get the trumpet out?..... it was a challenge trying to get it out along with the rain!..... ughh

I believe 33mm is the right size and 34 will work also.  The best advice I got from another person on this forum was not to bother with undoing that screw or using the compressor tool (most likely the threads on your cone are shot anyway).  Just take a recipricating saw and chop the trumpets which you are going to throw away anyway.  Before I did this, I tried the compressor tool with no success and had a hell of a time getting that big screw back in since the car body had shifted relative to the hole in the subframe that it threads into.  If you do end up doing the tool method, I would suggest to do one side at a time, and do all your jacking up BEFORE you take the big screw out. 

1-5/16"

I'm trying to get my front rubber cone out to install the new Spring shock.

My problem is what size socket do i need to remove the Screw that covers the cone where the cone compressing tool goes to compress the cone. I tried a size 32mm socket but that was to small.....