Question: During a battle between two extremely powerful space wizards, a beam of magical lightning has blasted a perfectly circular hole around 10 feet in diameter directly through an Earth-sized planet. In and out like a gunshot through paper. How would this impact life on the planet after this event, if at all?

NOTE: The incident occured about 150 miles south of the planet's north pole.

Answer: 
Immediate Effect
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You're going to get a pair of volcanoes. They might turn out fairly small, but I think there is a good possibility of super-volcanic eruptions. Consider this: the pressure around the surface of the solid inner core[1] is estimated to be around 330GPa (3.3 million atmospheres).

A supervolcano[2] erupts when the gasses dissolved in the magma come out of solution and I think this is exactly what would happen when a 3m diameter cylinder of earth, going right through the core, simply ceases to exist. Maybe the magma will quickly plug such an "insignificant" hole but I wouldn't bet on it; I suspect it would be more like a water-main break, where the jet of magma would continue to erode the hole for a long time.

Long-term Effects
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A typical supervolcano erupts with such force that large amounts of material (thousands of cubic km!) are launched into the atmosphere and disperse, to some extent, across the majority of the planet. The widespread particulate clouds can lead to a decrease in global average temperature. However, in this case such effects are likely to be more limited due to the type of eruption. I think of it inflating a balloon and then releasing the air from it rather than popping it... only the release of magma could continue for a rather long time. Instead of fizzling out with the hole plugging up, we might instead see the hole widen with magma flowing out for a Very Long Time (see Siberian Traps[3]). In this case, it could be nearly life-ending!

Summary
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* Probably (super?)volcanoes!
* Effects could range from "ooh, another volcano" to "where have all the plants/animals/people gone?"

[1] <https://en.wikipedia.org/wiki/Earth%27s_inner_core>  

[2] <https://en.wikipedia.org/wiki/Supervolcano>  

[3] <https://en.wikipedia.org/wiki/Siberian_Traps>
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> How would this impact life on the planet after this event, if at all?
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> 
> 

Say good bye to life.

An end to end hole on Earth would not be stable, and would collapse under the gravitational force exerted by the planet. That would alone would release a large amount of energy which would surely evaporate the oceans if not even melt the crust.

Add to that also the kinetic energy dissipated by the projectile when crossing through the entire planet, and the picture gets only worst.