Once you cut the Avocado it will last for 1 to 2 days.
You can store the cut up Avocado by putting it in plastic wrap or put it in an airtight container in the fridge to cut off air contact which makes it stay fresher during those 2 days.
If you keep the Avocado longer than 2 days then it begins to go bad so eat the cut up Avocado within 2 days or put the cut up Avocados in the freezer in an airtight container and you can still eat it or use it in things such as Guacamole or other dishes.
When you freeze the Avocados they lose their texture and fresh taste but go good with cooked foods or Guacamole.