Is relieving oneself after eating the same as throwing up to be patur from Benching? Perhaps it’s worth washing and making a new brocho?
The two are not the same. We are allowed to bentch as long as we are considered as having benefit from the food, which is until the food is digested and we would want to eat again (called “shiur Ikul”). This can be either 72 minutes or if the person ate a lot, it can be longer. After this amount of time, he may no longer say that bracha achrona. If someone relives himself during or right after eating, if it is during this amount of time, it is from other food that he ate during the previous meal etc., and it has no connection to this meal. Therefore he would not make a new bracha, but he would wash his hands.
On the other hand, when a person throws up what the food that he ate, even if it is during the meal he is no longer benefiting from the food that he ate, (unless he didn’t throw up all that he ate),therefore he wouldn’t say a bracha achrona. vomiting
Shulchan Aruch O:Ch 184-5, Sharei Teshuva O:CH 208-1, Shevet Halevi 1 203 comment on siman 208, PIskei Teshuvos 184-8, Orach Yisroel (Grossman) 19.