Granted, I haven't worked with SIR-models, but to me the answer is definitely nr. 1.
Fundamentally, $R_0$ is defined as the number of secondary infections from a single individual in an uninfected population. It is sometimes described as:
$ R_0 = \gamma *c * d $,
where $\gamma$ is the probability of transmitting the disease, $c$ is the average contact rate (encounter rate with other individuals), and $d$ the average length being infectious (which is $1/\beta$, there $\beta$ is the recovery rate). In your expression above $\alpha = \gamma*c$.
In this simple model of $R_0$ adding a mortality rate basically equates to adding another way of being removed from being infectious (you can either recover or die). Therefore, the expected time being infectious (previously $1/\beta$) is now the sum of two rates, $1/(\beta + \delta)$, where $\delta$ is the death rate (multiplying the two rates would be similar to estimating the probability that someone both recovers and dies from the infection). This means that $R_0$ with a death rate is:
$$ R_0 = \frac {\gamma c}{\beta+\delta} = \frac {\alpha}{\beta+\delta}$$
However, there are also more complicated (and realistic) ways of modelling situations with a death rate.
(I began my answer before @Artems nice answer, which is why I'm posting this as a complementary answer.)