If a battery driven device (a MacBook in this case) doesn't turn on without the AC adapter plugged in it means that the battery cannot supply enough current to power the device.
This first generation Macbook 12 inch was showing 75% battery remaining...
The "75% battery remaining" is a calculation based on how much charge the battery has verses it's full capacity and the electrical current it's capable of delivering at that moment.
When the battery drops below a certain amount of voltage, the overcharge/undercharge protection circuit kicks in and kills power to the device. What's happening with your battery is that it can no longer hold a charge. Even though it has calculated 75% charge left, the voltage drops too low too quickly and the MacBook will turn off/go to sleep.
Basically, your battery can no longer hold a charge and is going into hibernate/sleep mode. This is expected behavior.
This being a 2015 MacBook, it's unusual for a battery to have such a short lifespan, though it's not unheard of.
Batteries typically have a useful life of 3 to 5 years. So, less than 2 is concerning. If your product is still under warranty, you should get the battery replaced by Apple; it's covered under AppleCare if that is still in effect.
If you don't have AppleCare, it can still be fixed relatively inexpensively.
According to iFixit.com, the battery is glued into position and extremely difficult to remove. It can be done, but like I said - it's extremely difficult. Also, it's very difficult to source the part from reputable vendors.
However, the good news is that if you have the technical skill, you can replace the entire bottom case assembly (PN# 661-02245) for this unit as it includes the battery ($130USD at the time of this post). Ifixit.com has a guide for you to follow or you can take it into an Apple Repair shop.