I have some orders which need to be removed. In OrderServiceProvider class could not find any method related to deleting the order. Is there any other way to delete orders?
There is no possibility to remove Order by calling any API. There is no status for orders that could enable this.
Like anything else in Commerce, you can only change status of order. Records need to exist in DB for audit purposes.
Best status for you would be "Cancelled". No further processing of order is done afterwards. Keep in mind that order needs to be in "Pending" status before changing it to "Cancelled".
Take a look to chapter 5.1 of Developer Guide for further details -> http://commercesdn.sitecore.net/SitecoreXC_9.0/Developers-Guide/Sitecore-XC-9.0_Developers_Guide.pdf
I think there is no OOTB functionality to DELETE orders. Not in service provider of Commerce Connect not in Orders Manager of Business Tools, and not in Postman in the orders collection.
From what i can see this is still not supported in XC.
But you could directly go to SQL server into shared environment in the ordersentities table and delete the orders manually there. BUT this is dangerous and could produce sideffects if you delete it not correctly. Such an answer I also got from sitecore support some time ago in former versions.