That is all balogna (as my father used to say).
The daily freeze-thaw cycles of late winter and early spring trigger amalase to convert starches (stored in living cells) back into sugars. In maples a lot of this sugar gets dumped into the xylem lumens. Pressure builds up in the stem because of ozmosis of water. Cut or bore into the xylem and this sugar water (with some other, sometimes tasty compounds) 'gushes' out. Collected from sugar maples and cooked down, it makes a great syrup for pancakes and waffles. It even lends a nice taste to ham. Other maples, it seems, lack the traces of at least some of the tasty compounds.
Maples an trees are plants, not animals. They don't have a circulatory system - no pumps, no blood, and they don't really bleed in any sense other than figuratively speaking.