Summarize:

You can use any browser, such as Firefox or Safari, to access Discord. Though there's no real way to "ban" someone from a direct message, you can remove them from the group. Once banned, they'll no longer be a part of the conversation. If you haven't signed in, click the Login button at the top-right corner of the screen, type your account information, then click Login. All of your direct messages, including those with multiple people (group chats), appear under the "Direct Messages" heading. You'll find in the second column, near the left side of the screen. It's near the top-right corner of the screen and looks like two overlapping people. It's to the right of the pushpin icon. A list of people in the group will appear. A pop-up menu will appear. This person will no longer be a part of this group conversation.
Navigate to https://www.discordapp.com. Select the group message. Click the members icon. Click the person you want to remove. Click Remove from Group.