The day before churning, freeze the bowl of your ice cream maker.
Peel and slice the mango. Blend the mango until smooth in a food processor or blender. Measure out 1 cup of puree and transfer it to a large bowl. Add sugar, water, tequila, lime juice, and a pinch of salt. Whisk until the sugar dissolves. Chill the mixture for an hour in the refrigerator or 20 minutes in the freezer, stirring every 5 minutes to prevent freezing.
If making spicy strawberry jam instead of chamoy, mix jam and Tajin in a small bowl. Adjust Tajin to taste.
Dampen a paper towel with tequila and rub it inside your ice cream maker’s freezer bowl to prevent sorbet from freezing to the sides.
Freeze the mango mixture according to your ice cream maker's instructions until it has a soft-serve texture, about 20 minutes. Transfer spoonfuls of mango sorbet to a resealable container, alternating with spoonfuls of chamoy or jam mixture. Use a knife to swirl the two mixtures together.
Cover and freeze until firm, about 4 hours. Serve topped with more chamoy and/or Tajin if desired.