P.6.1- This is the first step of the turn during which any player receives priority. This means that any abilities that triggered at the start of this step, or during the Untap step are placed on the stack (see Rule T.2) at this time, then the current player gets priority to play spells and abilities. See Rule T.3 for details. [CompRules 1999/04/23]
P.6.Ruling.1- If an ability triggers at the beginning of upkeep, removing the permanent that generated that ability from play after that will not stop the ability from resolving (see Rule T.6). This means you cannot destroy a permanent in order to avoid its "at beginning of upkeep" ability. [D'Angelo 1999/05/01]