Cut off the top and bottom of the guava then remove the skin using a vegetable peeler. Cut into 4 vertical sections. Next, using a paring knife, slice out the midsections and remove the seeds. Grate into large shavings then let stand in a colander. Press with a spoon to release excess water.
In a medium bowl, combine yogurt, mint, olive oil, and cumin. Add guava and mix.