Acetone would take the finish off the wood piece.

How do you recommend using water to remove the glue? We don't want to damage the piece.

OP did not mention there was a finish, so IDK.

Scrape it off,that's what woodworkers do with squeeze out.

I am not familiar with the squeeze out product.

Would it work if I put a wet rag on the affected pieces and then tried to scrape it off?

Squeeze out is what we call the extra glue that is forced out of a glued joint. It is simply extra glue and is cleaned up with a damp cloth/towel.

Removing hardened glue can be removed several ways. The situation you have is one of the more difficult. To successfully remove most of the old glue, use a cotton swab soaked in water and held on the glue for several minutes. Acetone can also be used, but using too much will allow extra to drop on the finish and affect the finish. Acetone will 'melt' the old glue faster than water. Water will not affect the finish. So, you can decide which method to try.

Use a round/square toothpick(stronger than the flat kind) to remove the softened glue.

When all the glue that can be removed is gone, let the two pieces dry thoroughly and use an epoxy to reglue them.

Those who trained me as well as everyone I've worked alongside over the years remove old glue and dry squeeze out with a sharp chisel. I might have give up building and repairing furniture if toothpicks were all I could use to remove glue. I incourage aspireing woodworkers to have someone show them how,I believe they will be pleased with how little time it requires. The notion glue can be removed without damage to finish( if that's why toothpicks are reccommended) isn't possible. Instructions on glue usually state old glue must be removed and surface sanded or scraped to bare wood before applying fresh glue. I believe an antler tine is about as challanging as it get's so optimum prep is required. I dare say this antler might be beound the capability of me and several others that are attempting to tell op how it's done. Reality check,who amongst us will say they make attractive and lasting joints between wood dowel ends? The only use a toothpick might have here is being used as a tiny dowel inserted by experienced hands.

I actually have a set of chisels I use for removing glue squeeze out. I bought them years ago without looking to see they are metric.

I have done what I recommend, which is why I recommend the method. The repair was a wooden reindeer display I got for $5 because the owner could not fix it. I had to remove caked on glue(sometimes 3 layers, since he was persistent in failure).

Even my smallest chisel would have been a sledge hammer.

You will notice I recommended using epoxy instead of more glue. ;-)

OP is not about squeeze-out. It's about removing the old glue from jagged end-grain break (the way I understood it).

Casey

Sombreuil, yes, that is exactly what I am trying to do.

Here are photos of the piece that I am trying to repair.

That is a larger area than I envisioned(thanks for the pictures!).

Still use cotton swabs with water/acetone to soak, but now use a small brass brush to clean the residue.

Like this one

Vinegar and water also works to soften the glue, cover area with a rag wet with it and let it sit for a while, then pull it out with a tool like a dental pick. Might take several applications