It uses your Spell Save DC as it was when you cast the spell into the Guardian.
This feature for the Guardian says...
Spell Storing. A spellcaster who wears the shield guardian's amulet can cause the guardian to store one spell of 4th level or lower. To do so, the wearer must cast the spell on the guardian. The spell has no effect but is stored within the guardian. When commanded to do so by the wearer or when a situation arises that was predefined by the spellcaster, the guardian casts the stored spell with any parameters set by the original caster, requiring no components. When the spell is cast or a new spell is stored, any previously stored spell is lost.
Emphasis Mine from MM271
The spell's Save DC or Attack Bonus are parameters that go into a spell when you cast it. And these parameters are saved when you cast the spell into the Shield Guardian. The Shield Guardian is basically taking your spell and holding it in stasis until it is instructed to set it off.
This feature basically makes it a walking Ring of Spell Storing (DMG192)
Of note, these parameters are defined when you cast the spell, not when the Shield Guardian sets it off. So, if you cast a spell into your Guardian, then level up and your Spell Save DC increases--the spell stored in the Guardian is still using the DC you had when you cast the spell. If you want to use your new DC, you'll need to re-cast the spell.