A lot depends on the planet, but there are theories that as much as 3X the amount of water in the oceans is bound in mineral particles in the mantle. On Earth, this water is trapped in sediments and dragged into the mantle via the process of subduction, as sections of continental plates slide under other ones, only to reappear millions or billions of years later when magma bubbles back up to the surface in the form of volcanic eruptions.
If the planet in question already has active plate tectonics, then the solution would be to change the chemical and mineral nature of the sediments in the subduction zones so they could absorb a lot more water. This would allow some immediate lowering of the oceanic levels as the seabed becomes a sponge, than long term "storage" of the water as the sodden sediments are subducted into the mantel. The colonists will notice much more water vapour in volcanic eruptions @ 1,000,000 years in the future, but hopefully they will have used the time productively to prepare...
For a planet without active plate tectonics, the core and mantel wold need to be "reactivated", which would involve depositing huge amounts of energy deep below the crust. Since water itself is very good at absorbing energy, just setting up gigantic lasers or particle beam accelerators in orbit will result in boiling oceans, but not a lot of new tectonic activity. In the book "The Forge of God" by Greg Bear, malevolent aliens drop a slug of antimatter compressed to neutronium density into the Earth's core, which provides a fiery end to the Earth, but if you were to calibrate this properly and the energy release was less than the gravitational binding energy, then you should be able to melt the core and begin the process of plate tectonics (note, it will probably take thousands to millions of years for the heat to work its way from the core to the mantle and melt everything, so once again, this is a sort of long term project.
One thing which is not entirely clear is the role of the water in the upper mantel. Some scientists believe it acts as a sort of lubricant. If this is true then in the first case, the amount of movement between the plates could speed up (OMG, the continent has accelerated to 10 mm/year!), causing more earthquakes. In the second case, as heat percolates upwards the plates will remain locked together until a considerable amount of force is placed on them, resulting in even more massive earthquakes, until enough water is subducted into the mantle and a chemical equilibrium is reached.