The battery on a single charge will last for around 3-5 hours in workout mode and up to 5-7 days during standard use.
Swimmo's battery is rechargeable. The expected lifespan of the battery is 1000 charges, so the battery should last for several years.
Unfortunately, you cannot replace the battery. Swimmo watch has a display on the front, and the heart rate sensor on the back, so there is no easy way to do it by design.