2.5 feet per second per move action.

Mage Hand says:

As a move action, you can propel the object as far as 15 feet in any direction

Which means that the object can move as long as you have enough Move Actions to move it. Regardless of how fast you think that move action is, it cannot be longer than the 6 seconds that is the duration of a Combat Round.

So, the more move actions you use, the "faster" the object moves:

1. You have a Move Action every round.
2. You can downgrade a Standard Action to a Move Action.
3. You can use a Hero Point to obtain either a Standard Action or a Move Action.
4. You can use use the Pathfinder's Chonicler's Inspire Action to obtain another Move Action.
5. And any other ability that could grant your extra Move (or Standard) Actions.

With 2 move actions, the object moves 30 feet, or 5 feet per second (about 1.524 m/s).

With 3 move actions, the object moves 45 feet, or 7.5 feet per second (about 2.286 m/s).

With 4 move actions, the object moves 60 feet, or 10 feet per second (about 3.048 m/s).

And so on, increasing the speed by roughly 2.5 feet per second (or 0.762 m/s) per Move Action used to move the object.

P.S: No, it's not fast enough to hurt someone. That's what Telekinesis and Telekinetic Projectile are for. If the spell could cause damage, it would say so in its description.

In this case the range is probably measured from the hand itself

Normally, when you cast a spell that targets a location or creature that range is measured from the person who cast the spell. However there are exceptions.

Jeremy Crawford alludes to this in the following tweet:

Q: Call Lightning spell: on subsequent turns the point you chose must be within 120 feet from the point you chose for the cloud or a point within 120 feet from you? My doubt is born because, on susequent turns, you can move and go away from the fixed cloud above you

A: Call lightning is an odd spell because its range is measured from the effect it creates—the storm cloud—not from the caster.

Call lightning says:

When you cast the spell, choose a point you can see within range. A bolt of lightning flashes down from the cloud to that point. [...] On each of your turns until the spell ends, you can use your action to call down lightning in this way again, targeting the same point or a different one.

Which seems fairly similar to Maximilian’s Earthen Grasp which says:

You choose a 5-foot-square unoccupied space on the ground that you can see within range. A Medium hand made from compacted soil rises there and reaches for one creature you can see within 5 feet of it. [...] As an action, you can cause the hand to reach for a different creature or to move to a different unoccupied space within range.

Both spells create an effect which the spell allows to be moved on subsequent turns to target another creature/area.

If we follow Jeremy Crawford's ruling, I see no reason why Maximilian’s Earthen Grasp would not then follow the same ruling as Call lightning.

Thus, the range mentioned in the spell would be measured from the hand itself on every subsequent turn after the caster casts it.

So, as an action, the caster can move the hand up to 30 ft from the hand's current position (sort of like the hand had a move speed of 30 feet).