Good news! In Cutter v1.10 (December 20, 2019) the team introduced native and remote debugger support. By default, the STDIO of the debuggee is redirected to the Console Widget inside Cutter.
Downloading the latest release
To download the recent version of Cutter you can go to the official website and click on the Download button. It will automatically detect your OS and give you the right file to download.
Open Cutter and choose a file to analyze. On the following dialog configure the settings as you wish, you can leave it as-it for the defaults.
On the interface of Cutter you can start debugging by either of the following ways:
Press F9 to execute native debug
Click the green button at the top of the interface to start Debug
Click on the "Debug" menu and choose Start Debug
Then, click Play and the program will run. On Linux, you will see the STDIO in the Console Widget (open it from Windows -> Console). You can interact with it and send it input.