Removing radiator advise required

I have a radiator in the backroom of my house I need to completely remove, there's 2 windows and the radiator comes up in the middle of one and finishes in the middle of the other, now since I bought the house I've wanted to put French doors into the garden and decided the most cost effective way would be to put them where one of the Windows is, hence needing to rid the radiator, now the problem I have is that it's a concrete floor and I need to rid the pipes without smashing the whole floor out trying to find how they are routed, are there any solutions anyone can suggest to me please?

Dig up enough floor to be able to cut and cap the pipe, then cut the pipe and fit a cap to it

as muggles said but tidy up before showing the result