I think you can't use Groove weld in this situation because of chamfer.
I suggest modeling on part level and adding Label weld.
Here is a video about steps:
The weld features only really work well if the objects to be welded are flat and uniform. Like Imics said, you are best off making a model of the weld by doing a union intersection of the two pipes without the cuts and keeping just the intersection object.
I was able to get it to work if I used the Base Top-Path and Bas Bottom-Path buttons on the Command Bar.
Ater you click the two faces, go back and click the Base Face step button.
The target face seemed to get the edges for me automatically after I set the base edges.
It's like creating a lofted feature with 4 edges.
Lmics, thanks for the detailed video. That is a gerat solution and I will try it. Jason, how did you get the groove weld to work? It doesn't work for me. See video below.