Hi, welcome to OSM!
Are you using the edit function on openstreetmap.org?
The usual practice is to add a node where you want to split the way and split it there, either by
- highlighting the node, right-click on it and choose “Split”
- highlighting the node and pressing
X
in iD (the default editor on osm.org)
If you have any more questions, feel free to ask. Happy mapping!