Put the octopus in a pot with the wine and enough cold water to cover. Add the onions, carrots, celery, thyme, and bay leaf; bring to a gentle simmer over medium heat and cook until opaque, 20 to 30 minutes. Remove the octopus with a slotted spoon and cool. (This may be done a day ahead and refrigerated in a covered bowl.)
Transfer the octopus to a resealable plastic bag and add the garlic, olive oil, and lime juice; seal and marinate in the refrigerator for 2 hours. Remove the octopus from the marinade and set aside.
Preheat a charcoal or gas grill until hot. Position the rack about 5 to 6 inches from the heat.
Combine the olive oil, vinegar, lime juice, mint leaves, and green olives in the jar of a blender and puree into a smooth emulsion. Alternatively, whisk these ingredients together in a small bowl for a chunkier texture. Season, to taste, with salt and pepper and set aside. Toss the endive, radicchio, and chickpeas together in a salad bowl and set aside.
Grill the octopus for 4 to 5 minutes, turning once after 2 to 3 minutes, until it is browned in spots and nicely caramelized but not burned. Remove and cut into bite-size pieces. 0054oss with the greens and vinaigrette, divide among 4 plates, and serve.