Very high or very low dice rolls are unusual and signify good or bad fortune for the players.
The impact of Fumbles should take effect immediately and may not be negated through pushing the roll.
As is written on Page 89 of the keeper book,
"impact of Fumbles cannot be negated", but not "Fumbles cannot be pushed".
So does that mean if I take the effect of the Fumble (such as HP loss) , I can still push that roll?
A pushed roll is a second attempt (p.84), it's "not a re-roll; time always passes between rolls" (p.85)
I don't see a rule that would disallow a 2nd attempt when the first attempt is a fumble (once you take the consequence of the fumble), but as always the Keeper determines if a push is allowed to begin with.
Technically, mvincent is correct - the result of the fumble stands, but a second pushed attempt may be tried - if that fails, even more woe! But, it is perfectly fine if the Keeper rules that the fumble ends the attempt - another PC might then try, assuming they still have the ability to obtain the 'goal' desired from the roll.