Richard Moore wrote:

I have a cheap table saw with a riving knife that comes up over the top of
the saw blade.

This means I cannot do shoulder cuts for tenons as the wood above the blade
would hit the riving knife.

Would it be safe to cut the riving knife so that it stops just below the top
of the saw blade?

If it's a decent design, it shouldn't be difficult to remove it for the
occasions when it isn't needed/desired.