This question asks if the spell mage hand can catch thrown objects. But if you managed to place the mage hand in the way of a spell, such as fire bolt or magic missile, would the spell be blocked by the mage hand?
Magic Missile: no
This is the simple one; magic missile has no attack roll or saving throw, so nothing can stop it short of something that specifically calls out that it is capable of doing so (such as the Shield spell, for example).
Note how it just says:
Each dart hits a creature of your choice that you can see within range.
Firebolt: not really, but flavor, sure
Mage Hand does not specifically have any interaction with any attack spells, but there is a simple option available to everyone that lets you "block" Firebolt, which would be taking the Dodge action.
If you tell me "I'm taking the Dodge action and I'm going to try and block any incoming attacks with my Mage Hand" then sure, I'd let you do that. Of course, you could also take that action with an active Mage Hand and the result would be the same, but it's cooler this way.
The basic reason why the question has no real answer other than the above is that you ask "If you place it in the way of the spell", but the Mage Hand does not give any of its own mechanics for doing that, so mechanically you can't do it. At best, you can use some other mechanic to do roughly the same.
Note that if you want a giant hand that blocks attacks and enemies coming for you, you want Bigby's Hand, but that's a 5th level spell, not a cantrip, and it gives you an idea of how powerful something like that is.
Blocking magic missile is a function of the spell shield.
An invisible barrier of magical force appears and protects you. Until the start of your next turn, you have a +5 bonus to AC, including against the triggering attack, and you take no damage from magic missile.
There is a spell that can block magic missile, and it costs a 1st level spell slot and your reaction.
In general, since mage hand doesn't say it can block spells, it cannot block spells.
5th Edition has a "specific beats general" rule, which states:
If a specific rule contradicts a general rule, the specific rule wins.
Since magic missile states:
Each dart hits a creature of your choice,
each dart just hits the creature. To block magic missile a feature has to explicitly call out magic missile, as we see in the spell description of shield.
This applies in general as well, since mage hand doesn't say it can block spells as you describe, it cannot block spells as you describe - the spell description is the effect of the spell:
Each spell description in Chapter 11 begins with a block of information, including the spell's name, level, school of magic, casting time, range, components, and duration. The rest of a spell entry describes the spell's effect.
Since the spell description of mage hand does not include blocking spells, blocking spells is not an effect of mage hand.