It just so happens that on many of the servers I admin, the mysql dump files grow to be as much as a gigabyte per dump. But sometimes, only one or two tables need to be extracted, totaling just a meg or so.
Although several methods exist, this is one I happen to use quite often. Just a single line via awk will output the portion of the dump you are looking for.
In this example, table1 is the table you want to extract, and table2 is the table immediately following it.
$ awk '/Table structure for table .table1./,/Table structure for table .table2./{print}' old_dump.sql > /tmp/new_dump.sql