I'm not entirely certain if I'm am understanding you correctly but I think I am. After you have created the pipe you want to cut, the trick is to sketch a circle(or whatever shape the intersecting pipe is) onto a work plane, that is at the angle of intersection between the two pipes. You will probably want to create one work plane at the intersection of the two centerlines, at the angle of intersection and then offset another workplane from that one a distance that is greater than the diameter of the tube. This will let you cut all the way through without having mating issues later. Once you have sketched a shape on the offset work plane, you can extrude-cut that shape into your pipe. This should create a cut surface that will match up flush to the surface of the pipe you wish to mate to.
I'm sorry if this is confusing, I can send you an example part that should show you more or less what I am talking about if this isn't good enough.
Send me an e-mail and I will send you the part. dweber@api.com