Cap sealant leak *Help*

To be clear; you have a leak and it's damaging the wooden structure of the roof? If so, the answer to your question is that water is always way more invasive than it superficially appears. You're not going to remove the cap partially. It's fiberglass and one piece.  Roof decking under your TPO is often particle board which wicks moisture. Add to that, gravity is probably making your problem worse with water travelling down the inside walls. This picture looks like a pretty big leak with a severely neglected roof, and I'd guess it's been leaking for some time. If I were to bet, you're looking at replacing a lot of the front roofing and you're going to have to pull back the roof material to even get an understanding of the extent of the damage. You'll then have to replace some the roof decking, insulation etc. Looks like you have a TPO roof so there is a chance it can be laid back down, but to do it right you really should replace the whole roof material. But, that's all a guess from you're one picture. I won't even get into the mold remediation that should also be done.