"stifle late 14c., "to choke, suffocate, drown," of uncertain origin, possibly an alteration of O.Fr. estouffer "to stifle, smother," which may be from a Gmc. source (cf. O.H.G. stopfon "to plug up, stuff"). Metaphoric sense is from 1570s."
As Chris says, "stymie" has a different root to the above.
Stymie and stifle
"stifle late 14c., "to choke, suffocate, drown," of
uncertain origin, possibly an alteration of O.Fr.
estouffer "to stifle, smother," which may be from
a Gmc. source (cf. O.H.G. stopfon "to plug up,
stuff"). Metaphoric sense is from 1570s."
As Chris says, "stymie" has a different root to the above.
Andy.