EGODatabase*db=[EGODatabase databaseWithPath:[NSHomeDirectory() stringByAppendingPathComponent:@"Documents/database.db"]];
NSString*n=@"tableName";
NSString*sql=[NSString stringWithFormat:@"drop table if exists %@",n];
EGODatabaseResult*result=[db executeQuery:sql];
if (result.errorCode) {//failed
        
}else{//success
        
}

参考サイト
enormego/egodatabase · GitHub
https://github.com/enormego/egodatabase