Since mage hand cannot attack, would I be able to will it to pull a string tied to a trigger mechanism such as crossbow?
In order to do what you are talking about, the crossbow needs to:
- be mounted in a fixed location
- be pre-aimed at a spot where you hope the target will be when the crossbow fires
- have a string attached to the trigger mechanism in a manner that will fire the crossbow when the string is pulled.
What is being described here is not a weapon, it is a trap.
It is a trap that is triggered manually instead of automatically (such as by attaching the string to a tripwire), but it is still a trap.
If your DM allows you to use Mage Hand to remotely trigger traps that you find while exploring then there is no reason for them to disallow triggering your own trap the same way.
You should take a look at What are the options for player characters to create traps? for some rules and ideas about constructing traps.
Yes, assuming the crossbow is being held and aimed by someone or something else
The stat block for Mage Hand says:
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.
If you can open a door, grab an item from a bag, pour out a vial, or do any other object manipulation task, you can pull a string, even if it's connected to a crossbow trigger. So, what about the ban on attacking:
The hand can't Attack, activate magical items, or carry more than 10 pounds
By "Attack", this paragraph is referring to a specific concept in the rules. So, what is an attack? This question (What counts as an attack?) covers it in more detail, but the basic rule is this:
... the rule is simple: if you're making an attack roll, you're making an attack
So, you can certainly hold a sword or pull the trigger of a crossbow with mage hand, but you can never make a real attack that involves an attack roll against a target's AC. You can move and manipulate objects, including weapons, and, if the target is totally defenseless, for example cutting a sandwich with a knife or firing an aimed crossbow at a target, you might (with DM approval) even damage it, but if the attempt isn't an automatic success, then it would be an automatic failure (since you can't roll for the attack).
The mage hand cannot make an Attack (capital A, i.e. an attack roll).
- It could pull a pin that's holding the roof up.
- It could pull a lever that releases a trap door.
- It could trigger a crossbow by pulling a string.
They are all manually activating traps and get treated as such.
I think it's allowed
One interpretation is that the hand itself cannot hit a creature. Full stop.
This would allow for all sorts of things ranging from "I use the hand to drop Alchemist's Fire on such and such monster" to "I use the hand to hold a spear and then hit a monster with the spear".
Pulling the trigger of a crossbow seems fine under this interpretation.
...However, you might not want to
Mage hand isn't a sentient hand. It's an extension of your hand. How good would your aim be if you were firing a crossbow without being able to line up the sights on your target?
If I was the DM, I would impose a pretty large penalty to hit with a weapon via Mage Hand. And, don't forget, manipulating an object with Mage Hand costs your action.
Saying that Mage Hand can't attack at all is valid
All that said, your DM could rule that the spell can't be used for attacks at all. This would be a fair reading of the rules.