People often ask if we can cut heavy cardstocks using Cricut Joy. The answer is a definite YES, although you should always specify the thickness you are talking about.
Specifically, we have been recently asked how to cut 250-gsm pearl cardstock using Cricut Joy. We tried the 250-gsm kraft paper instead. Using Cricut Joy's "Heavy Cardstock" material setting, we are able to have a very clean cut.
Please watch it on our YouTube channel here:
Important points to note in cutting heavy cardstocks (applies to any Cricut smart cutting machines):
Use a mat in good condition. If part of the mat got worn out and lost its tackiness, the paper would shift (locally) when that region is cut. This would result in either un-clean cut or complete failure.
Use a brayer to make sure the entire piece of paper is adhered well on the mat. Same reason as above.
Use a setting with multiple cuts if necessary. The "Heavy Cardstock" setting actually runs the cut 3 times. You may create your own custom settings with desired force and number of cuts as you see fit for your materials.
Check if debris remains on the blade tip.
Cutting papers is actually challenging. You may need to try a few times to arrive at the desired material setting. With experience, you will get better at it.
Good luck and happy Cricut'ing!