Word that means "to remove dependence"

Solution 1:

I like "obviate", it means just what I was looking for. Could you please post it as an answer so I can accept it?

Done.

Definition of obviate

transitive verb : to anticipate and prevent (something, such as a situation) or make (an action) unnecessary.

Example: The new medical treatment obviates the need for surgery.

Solution 2:

I don't mean to restate your example, but "eliminating" sounds like a fine option. Unless you are looking for more dramatic portrayal of the accomplishment, á la infomercial, then using forms of abolish or vanquish. Eradicate and alleviate are also possibilities, again dependent on exact context (i.e., marketing or solely explanatory). Remedying, unfettering evoke more of the liberation of something restrictive.