A) There are two options that allow you to show only your own buffs and debuffs (one option for each), see Slim_Config.lua.
Code:
cfg.onlyShowPlayerBuffs = false -- only show buffs casted by player (target and focus)
cfg.onlyShowPlayerDebuffs = false -- only show debuffs casted by player (target and focus)
B) Or you could use the aura filter (that is used for raidframes), by editing Slim.lua. Which would only show white-listed buffs/debuffs that are listed in Slim_AuraFilterList.lua (you can add/remove buffs/debuffs there).
Put in the following code in the "target's section" (somewhere AFTER line 1226 and before 1282). A text editor like Notepad++ will show you line numbers.
Code:
self.Buffs.CustomFilter = CustomFilter
self.Debuffs.CustomFilter = CustomFilter
B - is probably more what you want, since it allows you to see only relevant auras you want to see (via the filter list). Hiding everything else.