No, you can not descend from your assigned altitude until specifically cleared by ATC to descend. But yes, you can descend down to your Approach without further clearance given you meet a few parameters
First, make sure you are cleared for the Approach itself and not just cleared direct to the waypoint. Your assigned altitude is mandatory until you are established on your cleared Approach. Established means that you are on or immediately about to be on (less than a mile of) a published leg of the Approach. Once you are established on your published leg, you can descend to the at or above altitude published for the route.
If the altitude has a line above and below it, you must be exactly at the published altitude. If that is the case, you will be verbally stepped down to the altitude by ATC.
If the IAP includes a published Terminal Arrival Area, and you are cleared for he Approach, you are considered established on the approach when you are inside of the TAA’s lateral boundaries. The altitudes published for the TAA will dictate your altitude limits you have to remain above.
If ATC does not expect you to follow the IAP exactly to include its published altitudes, they will not clear you for the Approach. They will continue to vector you and give you altitudes.