First, you need to give 2 months notice to cancel insurance in Spain so don't wait until your renewal date.
Second, if you have a mortgage you do need buildings insurance. If you have this through the bank you are probably paying well over the top as they are taking a cut.
We are also non resident. We cancelled our insurance policy (put in place by the bank along with the mortgage) and now use Op de Beeck brokers. They communicate in English and were very helpful, showing all the options for contents insurance for owners use/rentals/type of cover/length of time the apartment is empty etc. They also recommended standard buildings cover for pur size of apartment in a block, whereas the bank had arranged cover for the full amount of the mortgage. We're on our second year, they contacted us in good time to renew our policy and again gave us a range of options and we were able to change provider and save a bit of money.
The bank did try to tell us that we couldn't make this change, and we did have to name the bank as an interested party on the buildings insurance cover but otherwise we have saved a lot of money and have better cover with good information and ease of contact with the insurer.
Other owners on our site use Intasure although there are negative reviews on the web about them. We have claims going on with Intasure and Op de Beeck as well as Generali Seguros at the moment after some break ins, will be interesting to see if anyone has any problems with their claim. Generali Seguros are another big spanish company who have English speaking staff, and have paid out on claims with no problems.
If you do have any need to claim on the buildings side, the insurance assessor will determine whether the problem is yours or a matter for the community insurer. I assume that the two insurance companies will argue re liability if it is an issue.
I hope this helps.