Yes. Red-eared sliders are known to be very independent creatures, and thus if you disturb them when they want to be alone, they will very likely bite. Turtles in general are known to bite, especially when you touch them around their heads, which are very sensitive areas. If you want to avoid being bitten, then you should make sure to only ever handle red-eared sliders with the utmost care, so as to avoid touching any sensitive or painful spots on the turtle’s body.