No, this is basically shoving
While this is a clever idea, this isn't something that you can do with mage hand. The spell limits your interactions with (emphasis mine):
You can use your action to control the hand. You can use the hand to manipulate an object, open an unlocked door or container, stow or retrieve an item from an open container, or pour the contents out of a vial. You can move the hand up to 30 feet each time you use it.
The hand can't attack, activate magic items, or carry more than 10 pounds.
Why is tripping shoving?
Mechanically, I think there is only one ability that 'trips': The Battle Master Fighter's Trip Attack
When you hit a creature with a weapon attack, you can expend one superiority die to attempt to knock the target down. You add the superiority die to the attack’s damage roll, and if the target is Large or smaller, it must make a Strength saving throw. On a failed save, you knock the target prone.
Functionally, this is basically adding a shove attack added to a weapon attack. But the Shove is a specific attack action that requires an attack action.
Using the Attack action, you can make a special melee attack to shove a creature, either to knock it prone or push it away from you. If you're able to make multiple attacks with the Attack action, this attack replaces one of them.
The target must be no more than one size larger than you and must be within your reach. Instead of making an attack roll, you make a Strength (Athletics) check contested by the target's Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the ability to use). You succeed automatically if the target is incapacitated. If you succeed, you either knock the target prone or push it 5 feet away from you.
The mage hand can't attack, and the target is definitely going to not fulfill the size requirements either.
There's a lots of things you can do with mage hand, but this isn't going to be one of them.
Tripping a fleeing enemy
Let's say that your character wants to do this, though (just as an exercise.) In order to trip them as they flee, you'd need to ready your action to do this as they passed by. This allows you to use your reaction as they run by you. But if you're in range to trip, then you're also in range to attack. Attacking for damage may be the better option. If the trip is successful, all you've done is required them to use half their movement to stand up. This will prevent them from moving as far (by half their movement), but it won't stop them from leaving in general.