I made a mistake to describe it, but i don't know how you call the side "material" alike spider of the paper cone.
Yes, if spider damaged, it's easy to replace a new.
The spider is MUCH harder to replace than the surround (which is the tear in question). If you are going to try to "replace" a spider-you are much better off doing a full recone.
However replacing the surround is not a big deal-I used to do that all the time (when I was a reconer) for various rips and tears-and it was cheaper than a full recone.
Of course you have to have the skill and knowledge of how to do it properly-or the speaker will end up worse than when it started.