The 29-year-old challenged her anger to secure a fourth- round win over Hsieh - who had shocked world No. 1 Simona Halep in the previous round.
"No, I understand. You know, she's a fighter".
"I still have a long way to go to be where I was".
Ostapenko's second Grand Slam semi-final appearance will be against former Wimbledon finalist Angelique Kerber on Thursday.
Now she played in the quarters of Wimbledon for the first time against the experienced former No1 Kerber, who was runner-up here in 2016-the year she won both her Majors. The young Latvian was no stranger to this part of the tournament either: She went on from Paris to reach the quarters here, and looked formidable in equalling that run this year.
Jeļena Ostapenko became the first Latvian to reach the Wimbledon singles semifinals after she subdued Slovakia's Dominika Cibulková 7-5 6-4 on Tuesday.
Goerges had suffered five successive opening round defeats at the All England Club before this year.
This is only her fourth tournament since giving birth to daughter Olympia in September 2017, and the 23-time Grand Slam victor pointed out how motherhood had changed her approach to tennis.More news: North Korean officials snub meeting on United States soldiers' remains
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Yet to drop a set, she credits her grass court preparation at Eastbourne the week before the Championships began for getting her ready: "I just practiced really well before Eastbourne, then played Eastbourne and came here".
"I think we both played on a really high level, starting from the first point", said Kerber.
It also proved beyond doubt that she is the woman to beat in the women's draw, despite this being just her fourth tournament back since giving birth last September.
Williams' seemingly inevitable march to the final of a women's singles tournament in which none of the top 10 seeds remain continued at pace against Evgeniya Rodina as she eased into the last eight, but the seven-time Wimbledon champion needed to use much more of her reserves against Giorgi.
No. 11 Angelique Kerber faces 12th-seeded Jelena Ostapenko in the other semifinal. "But whatever happens it's a great moment for me and incredible motivation to keep going for the rest of my career", Serena added.
Given the opportunity to criticise Cibulkova for protesting about the replay, Hsieh took the high road.
Kasatkina finished with seven double-faults, including one on break point in the second game and then two straight to hand Kerber a 5-3 lead in the first set - halting her momentum just after breaking to get back on serve with the help of one of the best rallies of the match. "I'm fighting until the end and I'm gaining more confidence".
Argentina's fifth-seeded Juan Martin del Potro overcame Frenchman Gilles Simon 7-6 (1) 7-6 (5) 5-7 7-6 (5) in four hours and 24 minutes to set up a quarter-final contest with Rafa Nadal on Wednesday. On one particularly insane 40-all volley, the two volleyed 25 times before Kerber got it to match point - which Kasatkina quickly reset to 40-all.
However, the 14 errors meant that Kerber, at the third attempt, broke to lead 4-3.