Set up your grill and heat up your coals.
When coals are almost ready, toss mushrooms caps in oil and garlic. Set stand for a few minutes. Place mushroom slices onto grill. Cook for about 3 to 5 minutes.
Meanwhile, combine the ingredients for the Pico de Gallo. Season with salt and let stand for a few minutes.
Squeeze lime over the mushroom slices and then sprinkle with some salt. Flip and cook for another 1 to 2 minutes and squeeze more lime and salt over slices.
Heat tortillas on open section of grill while mushrooms finish up, about 1 to 2 minutes.
Remove tortillas from the grill. To assemble, place a few slices of the mushrooms on a tortilla, top with Pico de Gallo and sliced radishes, and serve immediately.