truncate sentence: delete up to, but not including period

t and f are nice when we are on the same line. If the period is on another line, we're back to /\.. If you want to type ds, or cs, or ys, ... it can be done thanks to an operator-pending mode mapping:

:onoremap s /\./<cr>
" and for visual mode, with e-1 to exclude the period.
:vnoremap s /\./e-1<cr>

But honestly, I'll bind this to . instead of s as s already does something in visual mode.

You had the right idea with df.. Of course, f goes up to the period like you noticed. If you use t (mnemonic until) instead, it will go forward until the period, but not to it. From :h t

                            *t*
t{char}         Till before [count]'th occurrence of {char} to the
            right.  The cursor is placed on the character left of
            {char} |inclusive|.
            {char} can be entered like with the |f| command.

So if your buffer is like this:

Scholar X's monograph is a groundbreaking study but I don't like it.
                                               ^

and you type t., you will be here:

Scholar X's monograph is a groundbreaking study but I don't like it.
                                                                  ^

The f and t commands mirror eachother very nicely. In fact they're pretty much identical other than f moving one further.

• They can both be repeated with ; and ,

• They both have uppercase variants that move backwards instead of forwards

With no extra configuration involved, I would just use:

c).<Esc>

Bonus: It's repeatable with the dot command.

Also bonus: It works on any POSIX vi and is not Vim-specific.

And actually, I would use <C-[> (or "Ctrl+[" if you speak Windows) rather than actually pressing the "Escape" key.

In your case I would do the following:

ma)bd`a
^^^^^^^
||||||+ mark a
|||||+  line position
||||+   delete
|||+    go to end of last word
||+     start of next sentence
|+      mark a
+       set a mark

Although not one command as you ask, this does if you're used to using marks roll off the fingers with reasonable ease.

After reviewing the other answers I thought of this:

map ds v)2hx

Enter visual mode, go to the end of the sentence (even if on subsequent line), back up two characters to exclude the period, and delete.