Peel the mangoes with a vegetable peeler, then carefully cut the flesh away from the pit. The pit is shaped like an elongated disk, so you'll end up with two large oblong pieces from the flat side and two thinner pieces from the edge. Chop the flesh into 1/2-inch pieces and set aside.
Combine the pineapple juice, apple cider vinegar, palm sugar, garam masala, and cardamom in a 2-cup glass measuring cup or medium bowl. Whisk to dissolve the sugar.
Heat an 11-inch stainless skillet over medium heat for 2 minutes. Add the vegetable oil and swirl to coat the pan. Add the chili powder and mustard seeds and cook for 30 seconds, then add the onions and sweat for 3 minutes. Add the ginger and red bell pepper next and cook another minute. Follow with the mango, and finally stir in the salt and black pepper.
Pour in the juice mixture and bring to a simmer. Reduce the heat to low, cover the pan and cook for 30 minutes, stirring often.
When the cook time is finished, the mangoes should be softened and slightly broken down. Remove from the heat, stir in the raisins and cool to room temperature.
Enjoy the chutney immediately or transfer to a tightly-sealing jar (or several smaller jars) and refrigerate for up to 2 months.