From Minnisota DNR page
Ask the DNR
Q. In its statements on catch-and-release, the DNR says it's better to leave a deeply im-bedded hook in a fish's mouth and cut the line than to rip the hook out. The hook will supposedly dissolve. But how do biologists know this? en
A. There is no existing scientific research on the topic, but DNR fisheries biologists have observed fish surviving with hooks in various stages of "being dissolved" in their bodies. And many anglers have caught fish with a partially dissolved hook in its gut.
Many variables determine how fast the hook will dissolve, and if the fish will survive at all. These include hook location (throat, stomach, mouth, etc.), hook size, fish size, temperature (most reactions occur faster at higher temperatures, so a hook would probably dissolve faster in the summer than in the winter). A hook in the mouth may dissolve, but it could also work loose and fall out. A hook in the mouth might hamper feeding behavior, but only temporarily.
A hook in the gill, however, will almost always prove fatal because it interrupts the respiratory process before it gets a chance to dissolve. Hooks in the stomach will nearly always dissolve, if internal organs have not received life-threatening damage from the hook (such as during a fight between fish and angler).
How long does it take for a hook to dissolve? Again there are lots of variables, such as hook size and fish size. DNR fisheries biologists estimate that it would take roughly two to three weeks for an ?average? hook to be dissolved by the ?average? fish?without too much indigestion.
I often will kill a fish because it is gut hooked and bleeding. Stainless steel hooks of coarse will not rust out. Of coarse any fish deep hooked that is kept has no chance for survival.