is there anyway to start cassandra database without mounting database ?because file system is full
I will answer this in general terms as it is less of a Solaris question and more about database services and storage.
So in general, no, you won't be able to start a database that sits on a partition that has run out of space. However, that does not mean that there are not things you can do to get it started. Some things to look to do are:
1. Obviously - free up space (clear or archive old log files, they often share the same partition on database systems)
2. Add space to the existing partition (if you are using LVM for example, resize your volume by adding additional disk and expanding the filesystem it sits on - effectively solving the problem by doing #1 a little differently)
3. Reconfigure the DB so that logs are read/written to another partition that has space. Now that may mean you have to move the log director(ies) to another partition first unless you can live with starting new logs from scratch.
4. Reconfigure the DB itself to read the databases, tables and data from a different partition that has space. NOTE: this is the most risky since there are likely to be ownership and permission issues if you are not very careful and putting things back requires a repeat of the process.
Give whichever one of those you can a shot and let us know what happens!