Spectre is a DAG based (directed acyclic graph) distributed ledger (a structure as an alternative to blockchain based distributed ledger).
Is there any mechanism in Spectre to prevent sending spam transactions?
Sure, there is a desire to avoid unnecessary load. But it is futile apart from cautioning people to avoid hurting the system during its growth phase.
In a system without identities there is no way to apply quota or ratelimiting per participant, and global ratelimiting only results in a denial-of-service attack. In practice the only thing that prevents spam is a free market; if people want to pay more for something than others, it will get in. This is independent of the type of consensus algorithm used to construct the chain.