Stripboard/veroboard/matrix board design software
Frizting looks like the ideal tool for this:


Free (GPL license)
Multi platform (Linux, Mac OS, Windows)
Integrates a large library of components


The stripboard can be resized, you can chose the strips to be vertical or horizontal. You can also cut the contacts with your mouse like you would do in real life.

Example circuit:


Edit 30/10/2018:
Make sure you add a Stripboard and not a Perfboard, the Stripboard is the one circled by the dark red square on the following screenshot: (third item on the first row)