Because it’s a Resident Evil game, the sewers in Resident Evil 3 have increased security because they also happen to house a strange lab. Because of this, to get out, you will need to find a battery pack that can open the doors.
The first thing you will need to do is drop down into the disgusting sewer water, then slide down the incline to the lower level. We are going to go on a little detour now, to get some useful items before we go after the battery pack.
Check your map and take the path to the office. You are going to encounter a monstrous enemy called a Hunter Gamma. These are difficult to kill, and you need to wait until it is charging at you with its mouth open to hurt it properly. Use your shotgun to take it out, and be mindful because you will need to shoot this thing a lot to put it away.
When it is dead, continue on to the office. This is a safe room, so you can save your progress and then grab the MGL Grenade Launcher and the Explosive B compound. This is a great way to take out Hunter Gammas, and you will need to deal with some more of them to get the battery pack and get out of the sewers.
Leave the office and take the left route to get to the Lab. There will be more Hunter Gammas waiting for you. When you reach a scummy waterfall on the right, head through it to a partially hidden tunnel where you can find some ammo. Go back the way you came and take the other tunnel to get to the Lab. Here is where you will find the battery pack that allows you to get back out of the sewers.
Head back to where you initially dropped down to the lower level, and climb the ladder, then follow the stairs back up to reach the door you need to open. Be careful, though, because more monsters are waiting for you.
Remember, you will need to bring the battery pack with you, as you only get one. When you get through the door, take out the Hunter Gamma that jumps up at you, then turn left to the yellow iron door. Open it, walk down to where you used the battery pack, and grab it.