How to back up oracle database using java?

It depends on what you mean with "backup". If you want to create a dump of the database, you can do that using the dbms_datapump package.

As it is a regular PL/SQL package it can easily be called through JDBC. The easiest thing is probably to send an anonymous PL/SQL block as a single statement.

Something like this:

String sql = 
  "DECLARE \n" +
  "  handle NUMBER; \n" +
  "BEGIN \n" +
  "  handle := DBMS_DATAPUMP.OPEN(operation => 'EXPORT', job_mode => 'SCHEMA', job_name => USER||'_DUMP', version => 'COMPATIBLE'); \n" +
  "  dbms_datapump.add_file(handle => handle, filename => 'db_backup', directory => 'EXPDP_DIR'); \n" +
  "  dbms_datapump.metadata_filter(handle, 'SCHEMA_LIST', '''SCOTT'''); \n" +
  "  dbms_datapump.start_job(handle); \n" +
  "  dbms_datapump.detach(handle); \n" +
  "END;";
Statement stmt = connection.createStatement();
stmt.execute(sql);

Note that I left out any error handling. Alternatively you can call each dbms_datapump procedure individually (using a CallableStatement)

The dump will will be written on the server, not on the client!

For more details please refer to the manual:
http://docs.oracle.com/cd/E11882_01/appdev.112/e25788/d_datpmp.htm

Well, generally you can, because you can extract data and store SQL structure (tables, constraints, indices etc.) You may find useful this You can also use YAML format to store data.