How can I remove a bad execution plan from Azure SQL Database?
Azure SQL now directly supports this

Azure SQL Database directly supports clearing the proc cache of the current user database without any hacks:

ALTER DATABASE SCOPED CONFIGURATION CLEAR PROCEDURE_CACHE;


Additional Information

The following script (by Shannon Gowen) can be used to watch the process step-by-step:

-- run this script against a user database, not master
-- count number of plans currently in cache
select count(*) from sys.dm_exec_cached_plans;

-- Executing this statement will clear the procedure cache in the current database, which means that all queries will have to recompile.
ALTER DATABASE SCOPED CONFIGURATION CLEAR PROCEDURE_CACHE;

-- count number of plans in cache now, after they were cleared from cache
select count(*) from sys.dm_exec_cached_plans;

-- list available plans
select * from sys.dm_exec_cached_plans;