How to connect auto cut off circuit with battery level indicator?
I want to make a circuit which will auto cut off the power when the battery is full.


The LM3914 circuit opens the relay when the preset voltage has been reached. Use the relay contact to interrupt the charger current. Since both circuits are connected to the battery you should connect the negative of each together as a common ground (GND).


  By examining the number of LEDs glowing you can easily know the status of the battery. Suppose five LEDs are glowing. In this case, the battery capacity is 50 to 59%of its maximum value.


This is not correct. If 5 LEDs are lit your battery is (technically) flat.



Figure 1. Battery voltage over time at various discharge rates where 'C' is the amp-hour rating. The typical lead-acid discharge curve shows that battery voltage remains reasonably constant (at a given load) until the battery is almost fully discharged. Source: Glider Pilot Shop.

Studying the graph you will begin to see why battery management is a tricky subject. Depending on the load the battery terminal voltage will drop to a level depending on the internal resistance (which increases with age). After that it will very slightly slope downwards and then fall increasingly rapidly when nearly flat.

You could still get some benefit from the indicator by setting the scale to read from 11 V to 13.5 V in 0.25 V steps. To do this you would need to set \$ R_{LO} \$ (reference low) input to suit.



Figure 2. Expanding the scale for finer resolution over a narrower voltage range is covered in the LM3914 datasheet.

Also, since you are running this on a battery powered circuit you could switch to 'dot mode' to save power. For this just leave pin 9 open circuit.