1. Combine the poaching liquid ingredients in a large stockpot and bring to a boil. Add the octopus, reduce the heat to medium-low, and simmer until tender, 1 to 1½ hours. The meat is done when you can cut the thickest part of the tentacle with a butter knife. Remove from the poaching liquid and let the octopus cool for 15 minutes. Using your hands or a clean dishtowel, remove all the skin.
2. Combine the marinade ingredients in a medium bowl. Add the octopus, tossing to coat. Set aside at room temperature for 1 hour.
3. Combine the oil, lemon juice, vinegar, garlic, capers, olives, and raisins in a medium bowl. Salt and pepper to taste. Set aside.
4. Light a charcoal fire or preheat your gas grill on high. Oil the grill’s cooking surface.
5. Remove the octopus from the marinade, letting the excess drain back into the bowl. Discard the marinade. Season the octopus with salt and pepper and place on the grill. Cook for 5 to 7 minutes total, turning so that all the sides get slightly golden and crispy.
6. Remove to a cutting board, then cut the tentacles at an angle into ½-inch-thick pieces. Toss with the salad dressing. Add the arugula, radicchio, and basil, tossing well to combine. Serve immediately.