For the pineapple: Slice the pineapple into 1-inch rounds and place in a large bowl.
Mix together the lime juice, coconut rum, agave syrup and salt in a small bowl. Add the marinade to the pineapple and gently toss to coat. Cover and let marinate for at least 20 minutes.
When ready, preheat a grill or grill pan over medium heat. Brush the grill with the olive oil and grill the pineapple for about 3 minutes per side; there should be noticeable grill marks, but it should still be firm in texture. Remove to a serving platter.
For the whipped cream: Meanwhile, in the bowl of an electric mixer fitted with a whisk attachment, add the cream, agave syrup and the reserved lime zest. Whip until stiff peaks form, 2 to 3 minutes.
To serve: Top the grilled pineapple with generous mounds of the whipped cream, scatter over mint leaves and drizzle with agave syrup.