can you see the execution plan for this slowness, i.e., where the resources are consuming most.

Also just a suggestion to try, if you have select query in your SP, just run the query with hint.

Like select...............from tablename where conditions(if applicable)

with recompile.

Also try to recompile your SP. Might be stats are not updated in those table.

Check the index fregmentation level of the tables used in SP.