The ICommandManager interface is managing commands. So you can use it to get and execute commands.
You can get this from an IServer object.

It might be required for you to import the package if you encounter any issues (like casting an Array), so better be safe than sorry and add the import.
import crafttweaker.command.ICommandManager;

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<th>
  Type
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<td>
  Map<String, <a href="/Vanilla/Commands/ICommand/">ICommand</a>\>
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ZenGetter
commands

• int executeCommand(ICommandSender sender, String rawCommand);
• List<String> getTabCompletions(ICommandSender sender, String input, @Optional IBlockPos pos);
• List<ICommand> getPossibleCommands(ICommandSender sender);

To add your own command, look at CommandEvent