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Use a dictionary for substitutions.

The following should achieve the goal in the question.

sage: nvar = 10  # number of variables
sage: B = BooleanPolynomialRing(nvar, 'x', order='degrevlex')
sage: var = B.gens()
sage: var_sub = var[nvar - 1]
sage: var_sub
x9
sage: B.inject_variables()
sage: f = x0 + x1 + x7*x6*x9*x2*x0 + x6*x4*x3*x1 + x9*x7
sage: f.subs({var_sub: B.zero()})

Note that it prints out a deprecation warning about using order "degrevlex" with BooleanPolynomialRing.

DeprecationWarning: using 'degrevlex' in Boolean polynomial rings is deprecated.
If needed, reverse the order of variables manually and use 'degneglex'
See http://trac.sagemath.org/13849 for details.

Side comment: sing B.zero() is slightly neater (and faster) than using B(0).