An unseen servant is an object. It automatically fails it's save.
There are only three classes of target in the D&D rules: creatures, objects and locations.
AN unseen servant is a target; otherwise its AC and HP would not have been specified.
From the Making an Attack section:
- Choose a target. Pick a target within your attack’s range: a creature, an object, or a location.
From the Casting a Spell section:
A spell’s description tells you whether the spell targets creatures, objects, or a point of origin for an area of effect (described below).
An unseen servant is not a creature (it is mindless). It is not a location (it moves around). Therefore it is an object.
Objects always fail Strength and Dexterity saving throws, and they are immune to effects that require other saves.
If the unseen servant is in the area of effect of a fireball then it fails its save and is destroyed (since fireball always does more than 1 HP damage).
Additionally, an unseen servant is invisible so cannot be targeted by any feature that specifies "that you can see". If you attack it, you roll at disadvantage because you can't see it - but you can still attempt the attack. If you hit AC 10 and do at least 1 HP of damage then it is destroyed.