Hey Frenando,
As Hood said, that's not my work, I just posted the link cause I liked it.

I know very little about water jets.
What do you mean about "tangential" water jet.
A tangentil axis rotates about another axis.
What is the purpose of cutting beveled pieces? or can it cut straight sided pieces as well?
I don't know the purpose for sure but I'm sure it can cut straight sided pieces as well.
Can It be used to remove the taper left when cutting a thick piece with an abrasive water jet?
I'm guessing that is the whole purpose in setting it up as a tangential. Removeing or adding a taper/bevel as needed.
Brett