To delete a record using a cursor, simply position the cursor to the record that you want to delete and then call DBC->c_del().

For example:

#include <db.h>
#include <string.h>

...

DB *dbp;
DBC *cursorp;
DBT key, data;
char *key1str = "My first string";
int ret;

/* Set up our DBTs */
key.data = key1str;
key.size = strlen(key1str) + 1;

/* Database open omitted */

/* Get the cursor */
dbp->cursor(dbp, NULL, &cursorp, 0);

/* Initialize our DBTs. */
memset(&key, 0, sizeof(DBT));
memset(&data, 0, sizeof(DBT));
                                                                                                                               
/* Iterate over the database, deleting each record in turn. */
while ((ret = cursorp->c_get(cursorp, &key,
               &data, DB_SET)) == 0) {
    cursorp->c_del(cursorp, 0);
}

/* Cursors must be closed */
if (cursorp != NULL)
    cursorp->c_close(cursorp); 

if (dbp != NULL)
    dbp->close(dbp, 0);