No there isn’t a way, any more than there is a way to block “spammers” from accessing you home page. I mean you could put all kind of checks, but in the end you will break how sites are supposed to behave which will mean that someone somewhere will not get his content. If all you have is a blog maybe you just do not care as long as your friends and family can read it, but if you actually generate money with your site you might care more.
Instead of looking at logs you should ask yourself how come a request that should do nothing except for bootstraping wordpress is bringing down your site. If you run php 7+ and object cache the cpu cost of handling a “spammy” request should be close to zero. So either you should upgrade your server side to better gandle traffic, or you have a targeted attack against a specific plugin which tries to exploit its ajax handler, in which case identifying the target of the attack should be top priority. While an attack is unlikely, it still might make sense to change your log to show the payload of the request.