Use dtc, where c is any character, e.g. for you, you want dt"

This will delete upto but not including c.

If you had:

delete until exclamation point!

And the cursor was at the first space and you typed dt!, you would get:

delete!

Also dfc.

This will delete upto and including c.

Using df! on the same example above would give you:

delete

Just about any "motion" can be used for the d, c, y and similar commands.