Are there any tricks to put a 3" Tee into the main vent stack to add a lavatory? I don't think I can lift the top part of the stack up or push the bottom part of the stack down once I cut it in half but I think I'll need to seperate it by something like 2" and then push it back together to have enough room to slip in the tee... any help would be greatly appreciated.

If this is a basement lavatory the stack,(This is a cast iron stack isn't it?) you wish to discharge into isn't a "vent stack" it's a "soil stack" which means the lavatory MUST be vented.( if local codes allow you may use a AAV cheater vent instead of running a vent out the roof.)
Also why a 3" tee when it should be a 3X1 1/2 FIPS (female iron pipe size) threaded drainage tee. A 1 1/2" _PVC midland bushing will convert to PVC and you may arm out 3 1/2' to pick up the lav. If you wanted to go with a 3X 2" tee and midland bushing and arm out with 2" bushed down to 1 1/2"at the stubout you may increase the length to 5'.
Having said that let me show you how we cut a fitting in a cast iron stack. ( I can't believe you asked me how to cut into a stack and then failed to tell me what material I was cutting into.)
First we take the tee and place it against the stack with the center of the threaded branch at 17 1/2" off the floor. Mark the edges.
Now add 3/16 ths" on to each mark. Next we place a raiser clamp a few inches above the top mark and a bumper jack under one of the ears and jack it up to where it begans to take a strain. Make very sure it's solid and won't slip off. VERY SURE!!!
Next we take a set of cast iron ratchet cutters and make the top cut, then the bottom one and remove the cut piece. Now we place the metal sleeves and rolled back rubber gaskets on the open ends, (NO-Hub Couplings). Because we increased the cut by 3/16 ths" on both ends we now have enough room to slip the tee in, snap the gaskets up and tighten the No -Hub Couplings.
And that's how it's done. Good luck. Tom

Ok, I'm all new to this forum; my apologies for not giving you enough information! The soil stack (didn't know the difference between a soil stack and a vent stack until you explained it) is a vertical 3" PVC pipe and I'm trying to tie a 1 1/2" PVC pipe into that for the lav by using a tee. The lavatory IS going to be vented separately. How would I go about inserting a 3" x 1 1/2" tee into that vertical stack? I don't know how much I can lift the soil stack once I cut it. Your help would be greatly appreciated.

Here is an opinion from a non-expert, so you may want to wait to see what Speedball1 has to say.

As per his last post, you would want the tee at 17.5 off the floor. When I've put tee's into a PVC stack, I've always found that there is some play in the PVC such that I can force the top up an inch or so and the bottom down an inch or so. In my experience, after cutting out some of the PVC at the right height, that has almost always been enough to put a tee into the stack and have plenty left over to have enough PVC from the top and bottom stack piece in the tee to make a good solid PVC connection. If you find that the stack pieces don't move as much as you need, there are always rubber-like fititngs that you can generally bend into place and then the connection is made by screwing a metal band (provided with the coupler) tightly around the two PVC connections.

Always make sure you only cut out of the stack what you need and no more as you won't want to have to add PVC back to the stack to make the connection (does that make sense - it does to me, but I know what I am trying to say).

Good luck