I am not sure about your experience, but people come into and out of my professional life.  I know that business is business and we will not always agree.

So you can sever the ties with someone you do not want to remain connected to on LinkedIn.  Just delete them from your connections. They will not be notified.

But the sign of a healthy business life is the need to ask someone to reconnect with you, after the ill will or hurt has passed.

Ask someone to reconnect. Things change. You do too.

Indeed it can lead to something positive.  I was able to revive a connection today and also refer a new colleague to collaborate with that no-longer-severed-connection since the two of them had very specific areas of mutual interest.  I e-introduced them through LinkedIn. It felt good.