Originally I believed that there was no word for Earth-destruction in the English language, and felt that it was permissible to invent my own. Taking the prefix "geo-" meaning "Earth" and the suffix "-cide", meaning "kill", I formed the word "geocide".

It turns out the situation is rather more complicated than I first imagined. "Geo-" is a modern Greek prefix while "-cide" is an ancient Latin suffix, which doesn't match! Plus, the word "mundicide" already exists and has roughly the same meaning! What to do?

Words for Earth

• "Mundus" is Latin for "world" or "mankind" or even "universe", and gives the prefix "mundi-".
• "Cosmos" is the Greek equivalent of "mundus" and gives the prefix "cosmo-".
• "Terra" is Latin for "Earth", and gives the prefix "terra-".
• "Tellus" is also Latin for "Earth", and gives the prefix "telli-". Some Latin dictionaries imply that "Tellus" refers more to the Earth as a planet, and "Terra" refers more to the Earth as land, but the impression is that the words are pretty much interchangeable. In modern English, the "terra" prefix seems to have predominated.
• "Γαια" (transliterated "Gaia" and pronounced like "yeah") is ancient Greek for "Earth". That gives us the prefix "gaeo-". But in modern Greek the spelling has simplified to "geo-", and "gaeo-" now means "land" exclusively.

Words for destruction

• "-cide" is Latin for "killing", not "destruction", but this is a trivial point.
• "-ctony" is the corresponding Greek word for "killing".

Possibilities

Given these, we have the following possibilities:

• mundicide - a pre-existing word, although Dan Shaw writes, "The OED lists 'mundicidious', which is patently silly, obsolete and in fact only used over 350 years ago when inventing new and silly words was all there was to do of an evening (1647, N. Ward, Simple Cobler Aggawam [ed. 3] 20 'A vacuum and an exorbitancy are mundicidious evils')".
• cosmocide
• terracide - Starcraft fans are likely to already be familiar with this word
• tellicide
• gaeocide
• geocide
• mundictony
• cosmoctony
• terractony
• tellictony
• gaeoctony
• geoctony

I ultimately chose "geocide". It is obvious to most people what this means, and it didn't already exist, so I can claim credit for creating it. Also, while it is a combination of modern Greek and ancient Latin, there are plenty of these already in existence - the most notable being "television" - so there's no need to reject it on this score.