Mitch Wheatのコードを拡張すると、次のスクリプトは、制約を削除して動的に実行するコマンドを生成します。
declare @schema_name nvarchar(256)
declare @table_name nvarchar(256)
declare @col_name nvarchar(256)
declare @Command nvarchar(1000)
set @schema_name = N'MySchema'
set @table_name = N'Department'
set @col_name = N'ModifiedDate'
select @Command = 'ALTER TABLE ' + @schema_name + '.[' + @table_name + '] DROP CONSTRAINT ' + d.name
from sys.tables t
join sys.default_constraints d on d.parent_object_id = t.object_id
join sys.columns c on c.object_id = t.object_id and c.column_id = d.parent_column_id
where t.name = @table_name
and t.schema_id = schema_id(@schema_name)
and c.name = @col_name
--print @Command
execute (@Command)