Add SelectionChanged event and do like below to get selected item.
private void MainLongListSelector_SelectionChanged(object sender, SelectionChangedEventArgs e)
{
if (e.AddedItems.Count > 0)
{
YourListItemObject item = e.AddedItems[0] as YourListItemObject;
YourMainList.Remove(item);
}
}
EDITED:
private void Button_Tap(object sender, System.Windows.Input.GestureEventArgs e)
{
var element = (FrameworkElement)sender;
YourListItemObject data = (YourListItemObject)element.DataContext;
YourMainList.Remove(data);
}