Yes, they can. Show me in the Constitution where it says that you cannot propose amendments to a bill that are "non-related new stuff." You cannot.
An appropriations bill was duly passed by the House, and sent to the Senate for them to "propose or concur with Amendments." They proposed an amendment that struck every single word from the original bill.
Again, I understand that it isn't the spirit of the Founder's intention, but it is completely Constitutional under the letter of the law.
There was a move a few years ago (and at my age that could mean from the 1970s) to offer a Constitutional Amendment that bills could only be about one subject (no more unrelated pork spending bills attached to a bill changing the tax code, for example.) If that were passed, then the Senate could no longer change the original intent of a House revenue bill by striking the entire thing.
Well it must be that living Constitution attitude, that things change over time.