They are ordered according to the process of their correction or tikkun. Looking at the complete blessing will help to understand.
וְלַמַּלְשִׁינִים אַל תְּהִי תִקְוָה וְכָל הָרִשְׁעָה כְּרֶגַע תֺּאבֵד וְכָל־אֹיְ֒בֶֽיךָ מְהֵרָה יִכָּרֵֽתוּ, וְהַזֵּדִים מְהֵרָה תְעַקֵּר וּתְשַׁבֵּר וּתְמַגֵּר וּתְכַלֵם וְתַשְׁפִּילֵם וְתַכְנִיעֵם בִּמְהֵרָה בְיָמֵֽינוּ: בָּרוּךְ אַתָּה יְהֹוָה שׁוֹבֵר אֹיְ֒בִים וּמַכְנִֽיעַ זֵדִים:
The opening words are addressing those Jews who inform on their fellow Jews to the authorities of an oppressive, non-Jewish government. This type of government and those who make it up (וְכָל־אֹיְ֒בֶֽיךָ) we pray to become extinct, meaning that they and their potential future descendants end. They are enemies of G-d and His Kingdom.
We then address the next category of individuals who are called Rebels (הַזֵּדִים). Rebels can come from two general sources. Those who truly reject and oppose G-d, like for example Nimrod and his followers, and those who for a variety of reasons have been seduced. Those in the second category may be salvageable. There may be a possibility of rehabilitation for them.
And this illustrates the order of their tikkun.
The first group are connected politically and economically, powerful and exert their domination throughout society. For them we say the words:
תְעַקֵּר וּתְשַׁבֵּר וּתְמַגֵּר וּתְכַלֵם
Which mean: to uproot from power (they remain intact but separated from the source of their power), to shatter like one would split a log into kindling in order to ignite and burn it up (they are no longer intact), to overthrow or to diminish which means reducing their influence and their connection to the levers of power and finally to extinguish them and their influence entirely.
The remaining two terms in the blessing are:
They relate to those who have been seduced and may be salvageable and rehabilitated. Their seduction was possible because of character defects and their rehabilitation comes after first being removed from power. Only then can they potentially be rehabilitated by being humbled. The source of their seduction originates from pride. The final term is to subdue and again refers to the possible source of their seduction, overindulgence of their desires.