Fishing at the river today I caught a nice 5 or 6 on a frog.  It was taking me a while to get the frog out and I cut the line at the frog to get it out of the way and had the fish half in the water.  Got one side of the hook out and the fish decided to start fighting again and got loose with the frog still in it.

Nope. Only time I've ever cut the line to remove the hook is if the hook is in the gills and the easiest way out is to remove it out the gills instead of trying to come back through them.

I know I shouldn't have cut the line.  Before I cut it I was trying to get the frog out and my hand I slipped and grabbed the line without thinking and cut my hand and arm.  I just hate for that fish to be swimming around with that frog stuck in its mouth

Fish are pretty good at ridding themselves of a hook. 

11 hours ago, NoahWatts said:

I know I shouldn't have cut the line.  Before I cut it I was trying to get the frog out and my hand I slipped and grabbed the line without thinking and cut my hand and arm.  I just hate for that fish to be swimming around with that frog stuck in its mouth

Don't worry about it, they've done a few studies on how long it takes for a bass to spit a lure out when hooked in the mouth that show that it takes at most a few days for them to eject the lure. Fyi, a jig was the lure that took the longest to eject and no bass tested failed to shake itself free from the lure imbedded in its mouth. I have actually witnessed this a coupe times in lakes with extremely clear water, once I broke a bass off with a jerkbait and watched it eject the lure within about five minutes (I was even able to retrieve my expensive jerkbait)  Have you noticed how quick a bass is to throw a lure when given slack? The same thing happens when they break your line.  I would be more upset about losing the frog.

I Hooked a bass on a jitterbug one morning before the sun came up.  I'm not sure if the knot was bad, or the line was damaged, but it broke and the bass got away.  About 45 minutes later when the sun came up, and we could see, my partner found my jitterbug floating at the bank,