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JavaScript

var arr = [{
	"roleId": "1",
	"name": "Superadmin",
	"permissions": [{
		"permissionId": "1",
		"action": "Remove"
	}]
}, {
	"id": "2",
	"name": "Administrator",
	"permissions": [{
		"permissionId": "1",
		"action": "Remove"
	}, {
		"permissionId": "2",
		"action": "Create"
	}, {
		"permissionId": "3",
		"action": "Read"
	}]
}];

var newArray = arr.map(function(obj){ 
  var rObj = {};
  rObj[obj.name] = obj.permissions.map(function(childObj){
     return childObj.action;       
  });
  return rObj;
});

console.log(newArray);