The Slime Diaries: That Time I Got Reincarnated as a Slime takes place in the same universe as That Time I Got Reincarnated as a Slime, so I would highly recommend you to read/watch the main series first and then check the spin-off. Otherwise, it might be somewhat problematic for you to understand what is happening in the manga.

Anyways, The Slime Diaries: That Time I Got Reincarnated as a Slime takes a different approach and focuses more on the side characters, giving them the time to shine. Another thing to mention is that you will not see any epic fights whatsoever. The Slime Diaries shows more how Rimuru manages the city of Tempest. Simply put, it is a slice of life spin-off of That Time I Got Reincarnated as a Slime, but it focuses more on the life in the city, with many funny moments involved.

All in all, The Slime Diaries: That Time I Got Reincarnated as a Slime is perfect for casual reading. However, you need to watch/read the main series first, otherwise things might become complicated.