When Othello spies Cassio with the handkerchief, what does he want to do?

Iago has Othello hide in Act IV, scene i, in order to
watch him question Cassio about his whore.  Othello believes that they are talking about
Desdemona, while Cassio believes that the conversation is about Bianca, the harlot with
whom he is having a relationship.  The use of the pronoun "she" is most convenient here
for Iago.

During the course of this, it is most fortuitous
to Iago's scheme that Bianca comes storming in with Desdemona's handkerchief
saying:

This
is some minx's token, and I must take out the work?  There!  Give it your hobby-horse,
wheresoever you had it...

And
she apparently throws the handkerchief at Cassio.

Upon
hearing this, Othello puts two and two together and arrives at the assumption that
Cassio has received the handkerchief from Desdemona and given it to his whore.  His
response when Cassio leaves and he comes out of hiding
is:

How shall
I murder him, Iago?. . .I would have him nine years a-killing. . .And let her rot and
perish and be damned to-night, for she shall not live. .
.

He more than wants to kill
both Cassio and Desdemona, he plans on it.