The 69th-ranked Knapp didn't face a break point and converted all five chances to break Beck's serve. Beck had beaten Knapp in straight sets in Nuremberg last month.
Knapp, who also reached the semis in Slovakia and Colombia, will play Yvonne Meusburger of Austria for a place in the final.
Meusburger, coming off her second career final in Budapest last week, defeated Arantxa Rus of the Netherlands 6-1, 7-6 (1). The Austrian failed to serve out the match at 5-4 before converting her first match point in the tiebreaker.
Svitolina defeated Patricia Mayr-Achleitner of Austria 6-3, 6-0. Hlavackova reached her first career WTA semifinal by beating Austrian wild card Lisa-Maria Moser 6-3, 7-6 (4).