The incidents are being investigated as a possible murder-suicide.
The woman was in her 60s; the son in his 30s.
Authorities have not yet recovered a murder weapon.
The woman was found dead on the pavement outside an apartment building, CNN affiliate WCBS reported. She had been decapitated.
“I literally thought it was a prank,” one resident said, according to WCBS. “We saw the body on one side and saw the head on the other side. I thought everything was a prank.”
Less than a half hour after the body was found, a man in his 30s was struck by a Long Island Rail Road train from Penn Station in Manhattan, WCBS reported.
“It’s insane,” a Farmingdale resident said, according to WCBS. “You never think something like that’s going to happen right outside your doorstep.”
The names of the man and woman have not been released, Nassau County police said. The investigation is ongoing.