The church condemns artificial birth control because it violates God’s will in our life cycle. Should not the same logic condemn mechanical interventions and organ transplants?

When an artificial device such as a knee replacement is used, or in the case of an organ transplant, we are seeking to repair something which is no longer working properly. However, in the case of contraception we are seeking to render dysfunctional, something which is functioning properly, and is a normal aspect of a healthy body. This is a rather big difference and renders your example more of a contrast than a comparison.
 
Further, it is too simplistic to say that the Church condemns artificial birth control merely because it violates God’s will in our lifecycle. It is more proper to say that the Church condemns artificial contraception because it violates our obligation of safeguarding both the unitive and the procreative dimensions of the conjugal act. In other words, contraception violates the intrinsic meaning of human sexuality.
 
The replacement of a knee or a kidney however, does not violate the essential meaning and purpose of the body. Rather, it helps to enhance the body’s overall function which has been diminished somehow, either by injury or disease.
 
There are of course limits to bodily interventions that we might make. There should be good reasons to replace organs or body parts, and our interventions should enhance the proper, God-given functioning of the body, not alter its intrinsic meaning. There are increasingly strange practices today involving exotic piercings, and extreme “body art,” some of which come close to mutilation and which may hinder the proper functioning of the body. So called “sex change operations” would also be excluded since they seek to fundamentally alter what God has given.
 
However, other things being equal, it is not inappropriate to make proper medical interventions to ensure proper and healthy functioning of the body.