Bu bavul benim değil = This suitcase is not mine.
Subject = bu bavul "this suitcase", predicate = benim değil "is not mine"
Bu benim bavul değil = This is not my suitcase.
Subject = bu, predicate = benim bavul değil "is not my suitcase".
Those two sentences essentially mean the same thing but are pragmatically very subtly different. It's possible to use suitcase in both parts of the sentence.
Bu bavul benim bavulum değil = This suitcase is not my suitcase.
... or in neither:
Bu benim değil = This is not mine.
Essentially, the structure of any of these sentences can be thought of as:
Bu (bavul) benim (bavulum) değil = This (suitcase) is not mine/my (suitcase).
You can mention the the word suitcase in either part of the sentence, but when you're referring to "this suitcase" it doesn't have a possessed ending and when you're referring to "my suitcase" it has -um.