A resonator can be replaced by a crystal as long as the crystal is the right type and of a sutiable frequency spec and you will need 2 small capacitors as well.
I can't see your clock so I haven't got a clue if it's OK. What does it look like? What frequency is it?
You can't just replace a resonator with any old crystal. So, a 4MHz resonator can be replaced with a 4MHz crytsal plus 2 20pF to 30pF(ish) capcitors. Or you can choose a faster crystal if you make adjustments to software settings where available.
I'm sure one the main PICAXE Data Sheets shows how to connect a crystal. Have a look.
If you are worried about the capcitor values then take a look at crystal manufacturer's data sheets - it's all there if you look.