I'm trying to use mongoDB with Morphia but still I have a problem with deleting documents. Is there any additional plugin or wrapper which works with Mongo and provides something like transactions in DBMS?
No, there are no (multi document) transactions. There are two possible solutions:
You can restructure your data into a single document instead of spreading it over multiple tables. Thus MongoDB's single document transactions (if you call them that) are enough for you. You can solve many problems with embedded entities or arrays. You might want to start a question related to "schema" design, if you're unsure how to approach this.
Your problem absolutely needs transactions across multiple documents / tables. Then MongoDB is simply not the right tool and you should use a relational database.
Don't fight the tool, pick the right one...