Does the Redmi Watch 4 support battery saver mode?

Yes.
For your reference, here are the ways to turn on the Battery saver mode:
1. Swipe up on the watch’s main page to open the control panel, and tap the Battery saver mode icon in the control panel;

2. When the watch pops up a 5% low battery reminder, there will be a [Turn on battery saver mode] option on the reminder page. Tap the option to turn on the battery saver mode.
Here are the ways to turn off the Battery saver mode:
1. After tapping the screen, rotate the crown according to the prompts to exit the Battery saver mode;
2. Place the watch on the charging stand to charge, and it will automatically exit the Battery saver mode.
Note:
While the watch is charging, it cannot enter Battery saver mode.