This is taken from the description of the Staff of the Woodlands (emphasis added by me):
You can use an action to expend 1 or more of the staff's charges to cast one of the following spells from it, using your spell save DC
What does "using your spell save DC" mean?
From the DMG at "Activating an Item" (p. 141):
Thus you calculate your DC as normal: 8 + proficiency bonus + spellcasting ability modifier.
If you don't have a spellcasting ability - and thus have no spellcasting ability modifier - then your spell save DC is just 8 + proficiency bonus + 0. (For the Staff of the Woodlands, which requires attunement by a druid, this is likely only possible for 13th-level Thief rogues, who have the Use Magic Device feature and can thus ignore class requirements on the use of the staff.)