Is there a way to split a mesh along a defined line that runs along polygon edges?

I guess the first thing is it possible to split a mesh along polygon edges,? I think maybe not, because I have tried it and they don’t seem to split if the cutting object falls exactly along edges?

I have resorted to deleting all the adjacent polygon faces along the edge to do this but it can be time consuming

Because when using extract faces you have to click each one , Is there any way to lasso faces or select them quickly?

Any thing I am missing maybe? Thanks

Command _SplitMeshWithCurve (Curve with degree 1) not work ?

Thank you Eddi, you know I have tried this in R4 and I remember I had problems with it. Now I just tried it in R5 and it is working. Wonder if this command has been updated in 5 or may be I was doing something odd in the past.