If it's a situation where you can't directly stop the person, like in a group setting, you can try to create a diversion. Maybe spill a little bit of water accidentally (not too much to cause a mess) and while everyone is distracted by that, try to steer the conversation in a different direction.
You could directly tell that person that it's a private matter and you don't want your mom to know about it. Be firm and serious.
You could directly tell that person how important it is to you that they keep it a secret. Be firm and serious about it.
Well, it might make her uncomfortable. Spanking is a rather sensitive topic and she might not want to hear about it. Also, she could get worried or think that there's something inappropriate going on.
You can be around your mom most of the time when she is with people who might know the spanking stories. That way, you can quickly intercept any conversation that might lead to those stories being told. Also, if there are certain events or gatherings where this could be a risk, you could give a general warning to everyone there in a light - hearted way, like 'Let's keep all the embarrassing stories to ourselves today, especially around mom.'
Tell them clearly that this kind of story is unacceptable and disrespectful to your family. If they continue, you may need to distance yourself from them as they lack basic respect for boundaries. Also, you might consider reporting their inappropriate behavior if it persists and makes you feel harassed.
She could be shocked. Moms usually have a certain image of how children should be treated, and spanking might go against that.
Have a serious conversation with your friends. Just be upfront and say, 'Guys, spanking stories are off - limits when it comes to my mom. It's a family thing and I don't want her to know about it.' Most friends will respect that if you're clear about it.
Because moms are often seen as more conservative or sensitive about sexual topics. Telling her sex stories might make her uncomfortable or even angry.
In this situation, it's important to approach your mom with respect. You can ask her what specifically bothered her about the discovery. It could be that she has different values regarding discipline. You can then talk about how you view these stories, whether as historical accounts or just something you stumbled upon, and assure her that it doesn't mean you support any form of inappropriate behavior.
Still be polite and listen quietly.