Deleting relationships doesn't serve any clear functional purpose to do casually, and may actually negatively affect aspects of the game, such as disrupting scoring counters of how many sims your sim has encountered for achievement purposes. The game already performs its own cleanup when a sim is deleted, anyway. I may consider it as a debug functionality. Just what kind of problem are you attempting to resolve this way?
I found that my relationship panel inflates itself pretty quickly with "acquaintance" relationships and tends to get pretty crowded/overstuffed with these. I found that simply ctrl-clicking the desired sims that I would never come in contact again with seemed pretty convenient and kept my relationship panel from getting over-bloated.
I understand some people may find this irrelevant and risky, but I'm sure lots of other people may find this handy like me!
Thanks for your consideration Pescado!