이전 종료시간과 이후 시작시간이 동일하네요.
시간의 연속으로 보고 결과물이 나오는 듯 한데요?
중간에 시간이 끊기는 경우는 없는지?

아래 쿼리의 RESULT 값을 원하시는 건가요?

WITH A AS(
    SELECT '2019-10-30 01:01:00' ST_TIME,    '2019-10-30 01:03:10' ED_TIME FROM DUAL UNION ALL 
    SELECT '2019-10-30 01:03:10' ST_TIME,    '2019-10-30 01:13:40' ED_TIME FROM DUAL UNION ALL 
    SELECT '2019-10-30 01:13:40' ST_TIME,    '2019-10-30 02:03:10' ED_TIME FROM DUAL UNION ALL
    SELECT '2019-10-30 02:03:10' ST_TIME,    '2019-10-30 02:23:54' ED_TIME FROM DUAL
)
SELECT
ED_TIME,ST_TIME,LEVEL*10 MINUTE
,ST_TIME+(LEVEL*10/24/60) RESULT
FROM( 
    SELECT
    MAX(TO_DATE(ED_TIME,'YYYY-MM-DD HH24:MI:SS')) ED_TIME
    ,MIN(TO_DATE(ST_TIME,'YYYY-MM-DD HH24:MI:SS')) ST_TIME
    ,FLOOR(((MAX(TO_DATE(ED_TIME,'YYYY-MM-DD HH24:MI:SS'))-MIN(TO_DATE(ST_TIME,'YYYY-MM-DD HH24:MI:SS')))*86400 /60)/10) CNT
FROM A
)A
CONNECT BY LEVEL<=CNT

WITH t AS
(
SELECT TO_DATE(sdt, 'yyyy-mm-dd hh24:mi:ss') sdt
     , TO_DATE(edt, 'yyyy-mm-dd hh24:mi:ss') edt
  FROM (SELECT '2019-10-30 01:01:00' sdt, '2019-10-30 01:03:10' edt   FROM dual
        UNION ALL SELECT '2019-10-30 01:03:10', '2019-10-30 01:13:40' FROM dual
        UNION ALL SELECT '2019-10-30 01:13:40', '2019-10-30 02:03:10' FROM dual
        UNION ALL SELECT '2019-10-30 02:03:10', '2019-10-30 02:23:54' FROM dual
        )
)
SELECT s + (LEVEL - 1)/24/60*10 x
  FROM (SELECT MIN(sdt) s
             , MAX(edt) e
          FROM t
        )
 CONNECT BY LEVEL <= (e - s) * 24 * 60 / 10 + 1
;