With projects, it means "to ruin" or "to destroy"
With theories or expectations, "to demolish" or "to shatter".

echar por tierra algo.
1. loc. verb. Destruirlo, arruinarlo.
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With theories or expectations, "to demolish" or "to shatter".

This would fit the example that I had:
El comandante Sanderson echó por tierra su argumento con una carcajada sarcástica.

Tad, I think the verb to dash is very close in meaning here, although it won't always be the best translation, since it sometimes sounds stuffy or old-fashioned.

The meaning lazarus gave I kind of quessed intuitively.
I suppose I find the 'por' confusing here, I know literal translations are not generally useful but if you had to translate it literally what would you say? 'Echó a tierra' to throw to ground' would for example make a little more sense to me.

Shooting from the hip here, but I'd say it means "throw all over the ground," presumably because the shards of what was thrown are scattered. Por can mean around, as in por aquí, around here, so that might be the nuance here. And that is the image conjured up by dash. "He dashed the vase to the ground." "He dashed Sanderson's argument." Again, there will usually be better translations, but it helps me to think of this Spanish phrase as being similar to "to dash."

Por can mean around, as in por aquí, around here, so that might be the nuance here.
Yes that helps to put it straighter in my mind, thanks both of you.