Symptoms

SLA Breakdowns by assignment table is empty 

Cause

Most probable cause: There is no record in "SLA Breakdown Definition to SLA Definition relation" table 

"SLA Breakdown Definition to SLA Definition relation" [sla_definition_sla_breakdown] is used for the relation between SLA Breakdown Definition and SLA Definitions. 
 

Its require to define for which SLA definition the breakdown to work

Resolution

Add relevant SLA definition entry in "SLA Breakdown Definition to SLA Definition relation" table. 
Then try creating task SLA record for that SLA definition. 

Relevant product doc: SLA breakdown definitions