Red Slimes deal a good amount of damage early-on in the game, especially without any armor.
The Red Slime moves identically to Orange Slimes - it hops in a short burst and has a decent cooldown period. You can use this period to either escape or deal large amounts of damage to one.
Avoid fighting several Red Slimes at a time early in your playthrough. You can easily get overwhelmed.
As with Orange Slimes, make sure to remove any Ground Slime in areas you would like to prevent Red Slime spawns.