At 12.47pm South Wales Police received a report that a woman in Allensbank Road has been assaulted and suffered a neck wound.
A second report was received at 12.51pm that a man had been assaulted in Tewkesbury Street.
The woman, who is in her 60s, was described as conscious and breathing at the scene and was taken to the University Hospital of Wales, Cardiff, for treatment. There is no update on her current condition.
The male victim, who is in his 30s, was described as being in shock after suffering facial injuries.
A man was arrested in Dalton Street at 1.12pm and a knife has been recovered.
More top news
Mark Ashley Hughes was found in possession of a sawn off shotgun and a Tazer. He claimed he found them in his grandparents garden.
Boater Nicholas Hodges was seen navigating erratically in Cardiff Bay on its way back to his mooring in the marina, court told.
Lily Connors has been awarded the world record with a staggering 6,641 items of Dr Who memorabilia.